XVII th Conference on Stochastic Programming

28 juil. 2025, 00:00 → 1 août 2025, 18:00 Europe/Paris

Bernardo Pagnoncelli (SKEMA Business School), François Pacaud (Mines Paris - PSL), Vincent Leclere (ENPC)

lun. 28 juillet

Registration

Welcome: Welcome Ceremony

Plenary session: Francis Bach

Président de session: Guanghui Lan (Georgia Tech)

1 Denoising diffusion models without diffusions

Denoising diffusion models have enabled remarkable advances in generative modeling across various domains. These methods rely on a two-step process: first, sampling a noisy version of the data—an easier computational task—and then denoising it, either in a single step or through a sequential procedure. Both stages hinge on the same key component: the score function, which is closely tied to the optimal denoiser mapping noisy inputs back to clean data. In this talk, I will introduce an alternative perspective on denoising-based sampling that bypasses the need for continuous-time diffusion processes. This framework not only offers a fresh conceptual angle but also naturally extends to discrete settings, such as binary data.
Joint work with Saeed Saremi and Ji-Won Park

Orateur: Francis Bach

fbach_diffusion_ICSP.pdf

2 A word about open science

Orateur: Michael Poss (LIRMM, CNRS)

12:30 Lunch

Stochastic Programming: Contributed talks

Président de session: Daniel Mimouni (Mines Paris / IFPEN)

3 Consensus, upgrade and skeleton clustering for stochastic programming

In stochastic programming, scenarios approximate distributions of unknown parameters, but in many applications the number of scenarios required to realistically model the uncertainty makes the optimisation problem numerically intractable. This motivates the scenario reduction problem: by finding a smaller subset of scenarios, reduce the numerical complexity while keeping the error at an acceptable level.

Recently, problem-based scenario reduction methods based on opportunity cost dissimilarities have shown to be effective. In this setting, opportunity cost means the cost of wrongly predicting scenario 1 when actually scenario 2 happens and can be viewed as a measure of how different these two scenarios are with respect to the optimisation problem at hand.

In this talk, I will discuss new distance matrices on the scenario set that are based on the idea of giving the decision maker some flexibility to change the first-stage decisions after the uncertainty has been revealed. We then apply clustering on the scenario set equipped with these distances.

Preliminary result indicate promising bounds and reveal interesting new structures on the scenario set.

Orateur: Janosch Ortmann (Université du Québec à Montréal)

4 Stable two-stage scenario tree generation via game-theoretic optimisation

Scenario generation methods constitute an important aspect towards efficient solution of Stochastic Programming (SP) problems and exploitation of big data. The ability of these methods to consistently provide scenario sets which guarantee stability on the solution of the stochastic programs is determinant of their performance. In this context, we present a modification of the existing Distribution and Moment Matching Problem (DMP) which is formulated as Mixed-Integer Linear Programming (MILP) model. The Nash bargaining approach is employed and the different statistical properties of the DMP are considered as players. Through this game-theoretic approach the impact of the user-defined parameters on the scenario generation procedure is investigated. Results from a capacity planning case study highlight the benefits of the proposed approach with respect to in-sample and out-of-sample stability.

Acknowledgements: Financial support from the EPSRC (under projects EP/T022930/1 and EP/V051008/1) is gratefully acknowledged.

Orateur: Dr Vassilis M. Charitopoulos (Department of Chemical Engineering, Sargent Centre for Process Systems Engineering, UCL)

5 Scenario Tree Reduction via Wasserstein Barycenters

Scenario tree reduction techniques are essential for achieving a balance between an accurate representation of uncertainties and computational complexity when solving multistage stochastic programming problems. In the realm of available techniques, the Kovacevic and Pichler algorithm (Ann. Oper. Res., 2015) stands out for employing the nested distance, a metric for comparing multistage scenario trees. However, dealing with large-scale scenario trees can lead to a prohibitive computational burden due to the algorithm's requirement of solving several large-scale linear problems per iteration. This study concentrates on efficient approaches to solving such linear problems, recognizing that their solutions are Wasserstein barycenters of the tree nodes' probabilities on a given stage. We leverage advanced optimal transport techniques to compute Wasserstein barycenters and significantly improve the computational performance of the Kovacevic and Pichler algorithm. Our boosted variants of this algorithm are benchmarked on several multistage scenario trees. Our experiments show that compared to the original scenario tree reduction algorithm, our variants can be eight times faster for reducing scenario trees with 8 stages, 78125 scenarios, and 97656 nodes.

Orateur: Daniel Mimouni (Mines Paris / IFPEN)

Application in energy, finance or logistics: New methods and applications of stochastic optimization toward logistics decarbonization

Président de session: Alexandre Jacquillat

6 Online Rack Placement in Large-Scale Data Centers: A Single-Sample Online Approximation Approach

This paper optimizes the configuration of large-scale data centers toward cost-effective, reliable and sustainable cloud supply chains. The problem involves placing incoming racks of servers within a data center to maximize demand coverage given space, power and cooling restrictions. We formulate an online integer optimization model to support rack placement decisions. We propose a tractable single-sample online approximation (SSOA) approach to multi-stage stochastic optimization, which approximates unknown parameters with one sample path and re-optimizes decisions dynamically. Theoretical results provide strong performance guarantees of SSOA in canonical online resource allocation problems. Computational results show that it can return near-optimal solutions and outperform certainty-equivalent benchmarks. Our algorithm has been packaged into a software solution deployed across Microsoft's data centers in collaboration with data center managers, contributing an interactive decision-making process at the human-machine interface. Using deployment data, econometric tests suggest a positive and statistically significant impact of our solution on data center performance, leading to 1--3 percentage point reduction in power stranding. The modeling and algorithmic solution developed in this paper can result in more efficient utilization of data center resources, resulting in multi-million-dollar annual cost savings and concomitant savings in greenhouse gas emissions.

Orateur: Prof. Alexandre Jacquillat (MIT)

7 A Stochastic Benders Decomposition Scheme for Large-Scale Stochastic Network Design

Network design problems involve constructing edges in a transportation or supply chain network to minimize construction and daily operational costs. We study a stochastic version where operational costs are uncertain because of fluctuating demand and estimated as a sample average from historical data. This problem is computationally challenging, and instances with as few as 100 nodes often cannot be solved to optimality using current decomposition techniques. We propose a stochastic variant of Benders decomposition that mitigates the high computational cost of generating each cut by sampling a subset of the data at each iteration and nonetheless, generates deterministically valid cuts, via a dual averaging technique, rather than the probabilistically valid cuts frequently proposed in the stochastic optimization literature. We implement both single-cut and multicut variants of this Benders decomposition as well as a variant that uses clustering of the historical scenarios. To our knowledge, this is the first single-tree implementation of Benders decomposition that facilitates sampling. On instances with 100–200 nodes and relatively complete recourse, our algorithm achieves 5%–7% optimality gaps compared with 16%–27% for deterministic Benders schemes, and it scales to instances with 700 nodes and 50 commodities within hours. Beyond network design, our strategy could be adapted to generic two-stage stochastic mixed-integer optimization problems where second-stage costs are estimated via a sample average.

Orateur: Ryan Cory-Wright (Imperial College London)

8 Incomplete-Information Inspection Game with Heterogeneous Resources

We study an inspection game of incomplete information, in which an inspector randomizes the allocation of heterogeneous detectors to identify multiple illegal commodities strategically hidden by an adversary within a system (e.g., drugs smuggled in containers). Detectors vary in their detection accuracies, and illegal commodities differ in their associated damage values. The inspector (resp. adversary) seeks to maximize (resp. minimize) the expected damage value of detected commodities, while facing uncertainty about the opponent’s resources. We analytically characterize the marginal detection probabilities and the expected damage values at each system location in equilibrium. We then design a polynomial-time algorithm to construct Nash equilibria by randomizing each player’s resource allocation to match these marginal quantities, subject to location-specific capacity constraints. Our equilibrium analysis offers inspection and security agencies actionable insights into optimal detector acquisition and the strategic value of adversarial intelligence.

Orateur: Mathieu Dahan (Georgia Institute of Technology)

9 The Surprising Performance of Randomized Partial Benders Decomposition

Benders Decomposition (BD) is a well-known optimization technique for large-scale two-stage mixed-integer problems by decomposing a problem into a pure integer master problem and a continuous separation problem. To accelerate BD, we propose Random Partial Benders Decomposition (RPBD), a decomposition method that randomly retains a subset of the continuous second-stages variables within the master problem. Unlike existing problem-specific partial decomposition approaches, RPBD is universally applicable and simple to implement. We present both computational evidence and theoretical analysis to demonstrate the efficiency and robustness of RPBD.

Orateur: Jean Pauphilet (London Business School)

Chance-constrained programming: Chance constraints in optimal control I

Président de session: René Henrion (WIAS Berlin)

10 Pontryagin's principle for some probabilistic control problems

Several problems in practice are described by a set of controlled state equations. If the problem moreover exhibits uncertainty, one can imagine these state equations to be parametrized by a random event or outcome. One may wish to control the final (random) state and ensure that it hits a desired region of space with large enough probability. Motivated by such a setting, we will discuss the derivation of a Pontryagin's optimality principle. The principle builds on (an extension) of recently developed differentiability results for probability functions. With both elements in place, we will also show how the resulting principle can be put to work.

Orateur: Wim van Ackooij (EDF Lab Paris-Saclay)

11 Inner Moreau Envelope of Nonsmooth Conic Constrained Probability Functions

Optimization problems involving uncertainty in the constraints arise in a wide range of applications. A natural framework for handling such uncertainty is through probability functions. However, these functions are often nonsmooth, which poses challenges for both analysis and computation. In this talk, we propose a regularization approach based on the Moreau envelope applied to a scalarization of the underlying vector inequality constraint. Specifically, we study a broad class of probability functions that encompasses many common forms of probabilistic constraints, where the inner constraint is expressed in a nonlinear conic form.

Our regularization method applies the Moreau envelope to a scalar representation of the data, yielding a smooth approximation of the original nonsmooth probability function. Under mild assumptions, we establish the smoothness of the regularized function and prove a form of variational convergence to the original probability function. As a result, for suitably structured optimization problems with probabilistic constraints, we can ensure that the minimizers of the regularized problems converge to those of the original problem.

We conclude by presenting illustrative examples and applications, including nonsmooth joint chance constraints, semidefinite chance constraints, and probust optimization problems.

Orateur: Pedro Perez Aros (Universidad de Chile and Center for Mathematical Modeling)

12 Consistency of sample-based solutions for stochastic optimization problems with conical constraints

This talk is concerned with a class of risk-neutral stochastic optimization problems defined on a Banach space with almost sure conic-type constraints. This kind of problem appears in the context of optimal control with random differential equation constraints where the state of the system is further constrained almost surely. For this class of problems, we investigate the consistency of optimal values and solutions corresponding to sample average approximation (SAA) as the sample size is taken to infinity. Consistency is also shown in the case where a Moreau-Yosida-type regularization of the constraint is used. The existence of Lagrange multipliers can be guaranteed under Robinson's constraint qualification with an appropriate choice of function space for the constraint. Our assumptions allow us to also show consistency of SAA Karush-Kuhn-Tucker conditions. This work provides theoretical justification for the numerical computation of solutions frequently used in the literature and in experimentation.

Orateur: Caroline Geiersbach (University of Hamburg)

13 Pontryagin principle for deterministic control of random semilinear parabolic equations with almost sure state constraints

We study a class of optimal control problems governed by random semilinear parabolic
equations with almost sure state constraints in the space of continuous functions. We
obtain necessary conditions of optimality in the form of a maximum principle with two
multipliers, one for the state constraint and one for the cost function, the multiplier
for the state constraint takes values in a space of measures. We prove the nontriviality
of the multipliers when the state constraint set has nonempty interior. Under a calmness
condition, the multiplier for the cost function can be suppressed.

Orateur: Dr Piero Visconti (INSA-Rouen)

Contextual stochastic programming: New frontiers for the sample average approximation in operations and statistics

Président de session: Bradley Sturt (University of Illinois Chicago)

14 Randomized Policy Optimization for Optimal Stopping

Optimal stopping is the problem of determining when to stop a stochastic system in order to maximize reward, which is of practical importance in domains such as finance, operations management and healthcare. Existing methods for high-dimensional optimal stopping that are popular in practice produce deterministic linear policies -- policies that deterministically stop based on the sign of a weighted sum of basis functions -- but are not guaranteed to find the optimal policy within this policy class given a fixed basis function architecture. In this paper, we propose a new methodology for optimal stopping based on randomized linear policies, which choose to stop with a probability that is determined by a weighted sum of basis functions. We motivate these policies by establishing that under mild conditions, given a fixed basis function architecture, optimizing over randomized linear policies is equivalent to optimizing over deterministic linear policies. We formulate the problem of learning randomized linear policies from data as a smooth non-convex sample average approximation (SAA) problem. We theoretically prove the almost sure convergence of our randomized policy SAA problem and establish bounds on the out-of-sample performance of randomized policies obtained from our SAA problem based on Rademacher complexity. We also show that the SAA problem is in general NP-Hard, and consequently develop a practical heuristic for solving our randomized policy problem. Through numerical experiments on a benchmark family of option pricing problem instances, we show that our approach can substantially outperform state-of-the-art methods.

Orateur: Xinyi Guan (The Hong Kong Polytechnic University)

15 From Contextual Data to Newsvendor Decisions: On the Actual Performance of Data-Driven Algorithms

In this work, we explore a framework for contextual decision-making to study how the relevance and quantity of past data affects the performance of a data-driven policy. We analyze a contextual Newsvendor problem in which a decision-maker needs to trade-off between an underage and an overage cost in the face of uncertain demand. We consider a setting in which past demands observed under "close by'' contexts come from close by distributions and analyze the performance of data-driven algorithms through a notion of context-dependent worst-case expected regret. We analyze the broad class of Weighted Empirical Risk Minimization (WERM) policies which weigh past data according to their similarity in the contextual space. This class includes classical policies such as ERM, k-Nearest Neighbors and kernel-based policies. Our main methodological contribution is to characterize exactly the worst-case regret of any WERM policy on any given configuration of contexts. To the best of our knowledge, this provides the first understanding of tight performance guarantees in any contextual decision-making problem, with past literature focusing on upper bounds via concentration inequalities. We instead take an optimization approach, and isolate a structure in the Newsvendor loss function that allows to reduce the infinite-dimensional optimization problem over worst-case distributions to a simple line search. This in turn allows us to unveil fundamental insights that were obfuscated by previous general-purpose bounds. We characterize actual guaranteed performance as a function of the contexts, as well as granular insights on the learning curve of algorithms.

Orateur: Prof. Omar Mouchtaki (NYU)

16 The Sample Average Approximation with Strategic Noise

We consider a pricing problem in which the buyer is strategic: given the seller's pricing policy, the buyer can augment the features that they reveal to the seller in order to obtain a low price for the product. We model the seller's pricing problem as a stochastic program over an infinite-dimensional space of pricing policies in which the radii by which the buyer can strategically perturb their features is a strictly positive random variable. We establish for this problem that the objective value of the sample average approximation converges almost surely to the objective value of the infinite-dimensional stochastic problem as the number of samples tends to infinity. This asymptotic consistency result shows that incorporating strategic behavior into an infinite-dimensional stochastic programming problem can, in addition to making the problem more realistic, help prevent the sample average approximation from overfitting.

Orateur: Prof. Bradley Sturt (University of Illinois Chicago)

17 ApplicationDrivenLearning.jl: A High-Performance Library for Training Predictive Models Based on the Application Cost

The Application Driven Learning is a framework that integrates the predictive machine learning model training directly with the decision-making processes, optimizing predictions specifically for the application context.

We present ApplicationDrivenLearning.jl, a high-performance Julia package that enables efficient experimentation and implementation of the framework, particularly for large-scale decision-making problems. The package allows users to apply the novel gradient-based heuristic and the two original methods: the heuristic based on Nelder-Mead and Bilevel Optimization. Moreover, the heuristics have also been parallelized with MPI allowing the user to optimize their models in high-performance computing (HPC) clusters.

To demonstrate the usage of the package, we present a case study contrasting the multiple implementations that are available to the users.

Orateur: Joaquim Dias Garcia (Soma Energy)

ApplicationDrivenLearning_jl.pdf

ML: Exploring the synergy between stochastic optimization, dynamics, sampling, inference, and optimal transport II

Président de session: Taiji Suzuki (The University of Tokyo / RIKEN AIP)

18 Convergence theory and application of distribution optimization: Non-convexity, particle approximation, and diffusion models

In this talk, I will talk about some recent results on distribution optimization methods. First, we will talk about a non-convex optimization technique for a Wasserstein gradient flow (WGF). While WGF is guaranteed to converge to a first-order stationary point, for nonconvex functionals the converged solution does not necessarily satisfy the second-order optimality condition; i.e., it could converge to a saddle point. To resolve this problem, we propose a new algorithm for probability measure optimization, perturbed Wasserstein gradient flow (PWGF), that achieves second-order optimality for general nonconvex objectives. PWGF enhances WGF by injecting noisy perturbations near saddle points via a Gaussian process-based scheme. We theoretically derive the computational complexity for PWGF to achieve a second-order stationary point and converge to a global optimum in polynomial time for strictly benign objectives.
Second, I present an improved error analysis corresponding to the propagation of chaos (PoC) for mean field Langevin dynamics (MFLD), where PoC provides a quantitative characterization of the approximation error in terms of the number of particles. In this study, we refine the defective log-Sobolev inequality---a key result from that earlier work---for a convex objective, and establish an improved PoC result that removes the exponential dependence on the regularization coefficient from the particle approximation term.
Third, if time permits, I introduce a novel alignment method for diffusion models from distribution optimization perspectives while providing rigorous convergence guarantees. The proposed method directly optimize the distribution using the Dual Averaging method and then adopt Doob's h-transform technique to generate sample from the optimal distribution. The proposed framework is supported by rigorous convergence guarantees and an end-to-end bound on the sampling error, which imply that when the original distribution's score is known accurately, the complexity of sampling from shifted distributions is independent of isoperimetric conditions.

Orateur: Taiji Suzuki (The University of Tokyo / RIKEN AIP)

19 Asymptotic log-Sobolev constants and the Polyak-Łojasiewicz gradient domination condition

The Polyak-Łojasiewicz (PL) constant for a given function exactly characterizes the exponential rate of convergence of gradient flow uniformly over initializations, and has been of major recent interest in optimization and machine learning because it is strictly weaker than strong convexity yet implies many of the same results. In the world of sampling, the log-Sobolev inequality plays an analogous role, governing the convergence of Langevin dynamics from arbitrary initialization in Kullback-Leibler divergence. In this talk, we present a new connection between optimization and sampling by showing that the PL constant is exactly the low temperature limit of the re-scaled log-Sobolev constant, under mild assumptions. Based on joint work with Sinho Chewi.

Orateur: Austin Stromme (ENSAE Paris)

20 Federated ADMM from Bayesian Duality

ADMM is a popular method for federated deep learning which originated in the 1970s and, even though many new variants of it have been proposed since then, its core algorithmic structure has remained unchanged. In this talk, we present a new way to derive and extend federated ADMM. We propose to use a structure called Bayesian Duality which exploits a duality of the posterior distributions obtained by solving a variational-Bayesian reformulation of the original problem. We show that this naturally recovers the original ADMM when isotropic Gaussian posteriors are used, and yields non-trivial extensions for other posterior forms. For instance, full-covariance Gaussians lead to a Newton-like variant of ADMM, while diagonal covariances result in a cheap Adam-like variant. This is especially useful to handle heterogeneity in federated deep learning, giving up to 7% accuracy improvements over recent baselines. Our work opens a new Bayesian path to improve ADMM-like primal-dual methods.

Orateur: Thomas Möllenhoff (RIKEN Center for AI Project)

Sequential decision-making under uncertainty: Contributed talks

Président de session: Michel De Lara (Ecole des Ponts ParisTech)

21 An approximate dynamic programming approach for multi-stage stochastic lot-sizing under a Decision-Hazard-Decision information structure

Lot-Sizing is a class of combinatorial optimization problems encountered in industrial production planning. This work addresses the stochastic capacitated lot-sizing problem with inventory bounds and lost sales. A production problem with uncertain demand is investigated with the assumption that decisions can be regularly updated to adjust to the actual demand being progressively revealed. We focus on a "Decision-Hazard-Decision" information structure derived from industrial applications, in which decisions are made at each stage both before and after uncertainty is revealed. The resulting multi-stage stochastic integer problem is particularly challenging to solve. Namely, the sub-problem to be solved at each decision stage is itself a two-stage stochastic integer program. Highlighting the shortcomings of existing methods to solve this problem, we propose a novel approach based on approximate stochastic dynamic programming. At each stage, the optimal production costs of all future stages depending on the final inventory value of the current stage are represented by a cost-to-go function. From the last stage to the first one, we dynamically construct a piece-wise linear approximation of these cost-to-go functions by solving successive two-stage problems. To further improve the overall solving time, an approximate model is introduced, and a scenario-based decomposition is implemented to efficiently solve each two-stage problem. In particular, a novel polynomial time algorithm for the resulting dual sub-problem is proposed to fasten its solving time. This decomposition method proves to be especially efficient for instances with a large number of uncertainty scenarios at each stage. Numerical results demonstrate that, even if the proposed approach is approximate, it offers practical benefits as it is able to provide production plans of good quality in record time for numerous cases.

Keywords: Lot-sizing, Multi-stage stochastic integer programming, Dynamic programming, Benders decomposition

Orateur: Victor Spitzer (Université Paris-Saclay (LISN) / Lhyfe)

22 Stochastic Dual Dynamic Integer Programming: finding better Lagrangian Cuts and application on energy planning problem

Energy planning plays a fundamental role in managing the generation resources in a power system. This planning must meet both present and future energy demands, considering various operational, electrical, environmental, political, and other constraints. The main objective is to allocate resources in a way that minimizes costs while mitigating risks associated with future uncertainties, ensuring the system's energy security.

Hydroelectric plants, which represent the main energy source of the Brazilian system, have operational constraints that lead to integer optimization modeling. These constraints can significantly impact the overall system operation. Therefore, it is crucial to accurately represent them in the optimization models used in energy planning to ensure time consistency, where the characteristics of the problem in future stages should be as close as possible to what will be implemented in the future.

However, the application of mixed-integer stochastic optimization for large-scale problems is still a developing field, especially when seeking detailed modeling of non-convex constraints. Thus, this work aims to identify and analyze various challenges related to energy planning, with an emphasis on mathematical modeling, solution algorithms, and computational robustness.

The main objective of this work is to explore the modeling of constraints involving integer variables in medium and long-term energy planning with an emphasis on the Stochastic Dual Dynamic Programming (SDDiP) algorithm. A conceptual evaluation of the cuts used in the SDDiP algorithm was carried out, focusing on the characteristics of the dual problem and the impact on the method's convergence rate. Based on this analysis, a methodology capable of obtaining more robust cuts is proposed. Results of the SDDiP method is applied in the context of stochastic energy planning, evaluating both the existing methods for constructing cuts and the proposed methodology.

Keywords: Energy Planning, Stochastic Optimization, Mixed-Integer Linear Programming, Stochastic Dual Dynamic Programming, Lagrangian Cuts

Orateur: Lilian Chaves Brandao (CEPEL/UFJF)

23 What Makes Information More Valuable? An Answer With Convex Analysis

In decision problems under incomplete information, actions (identified to payoff vectors indexed by states of nature) and beliefs are naturally paired by bilinear duality. We exploit this duality to analyze the interpersonal comparison of the value of information, using concepts and tools from convex analysis. We characterize each decision-maker (DM) by a closed convex lower set, the action/payoff set. Then, we show that one DM values information more than another DM if and only if their action/payoff sets are solution of an algebraic equation involving the Minkowski addition, and their star-differences. We present an application to the precautionary effect by analyzing various examples in the economic literature.

Orateur: Michel De Lara (Ecole des Ponts ParisTech)

Mini-symposium: Advances in two-stages robust optimization

Président de session: Michael Poss (LIRMM, CNRS)

24 Connections between Robust and Bilevel Optimization

Robust and bilevel optimization share the common feature that they involve a certain multilevel structure. Hence, although they model something rather different when used in practice, they seem to have a similar mathematical structure. In this talk, I present some connections between different types of robust problems (static robust problems with and without decision-dependence of their uncertainty sets, worst-case regret problems, and two-stage robust problems) as well as of bilevel problems (optimistic problems, pessimistic problems, and robust bilevel problems). It turns out that bilevel optimization seems to be more general in the sense that for most types of robust problems, one can find proper reformulations as bilevel problems but not necessarily the other way around. We hope that these results pave the way for a stronger connection between the two fields—in particular to use both theory and algorithms from one field in the other and vice versa.

Orateur: Marc Goerigk (University of Passau)

25 A semi-infinite constraint generation algorithm for two-stage robust optimization problems

In this talk we consider two-stage linear adjustable robust optimization problems with continuous and fixed recourse.
These problems have been the subject of exact solution approaches, notably, constraint generation (CG) and constraint-and-column generation (CCG).
Both approaches repose on an exponential-sized reformulation of the problem which uses a large number of constraints or constraints and variables.
The decomposition algorithms then solve and reinforce a relaxation of the aforementioned reformulation through the iterations which require the solution of bilinear separation problems.
Here, we present an alternative approach reposing on a novel reformulation of the problem with an exponential number of semi-infinite constraints. We present a nested decomposition algorithm to deal with the exponential and semi-infinite natures of our formulation separately.
We argue that our algorithm will lead to a reduced number of bilinear separation problems solved while providing a high quality relaxation. We further show that the classical mountain-climbing algorithm can be incorporated into our algorithm in a natural way.
We perform a detailed numerical study that showcases the superior performance of our proposed approach compared to the state-of-the-art and evaluates the contribution of different algorithmic components.

Orateur: Dr Ayse Arslan (Inria-Bordeaux/Institut de Mathématiques de Bordeaux)

ICSP-Arslan.pdf

26 Approximating Two-Stage Robust Optimization with K-Adaptability

In the realm of robust optimization the k-adaptability approach is one promising method to derive approximate solutions for two-stage robust optimization problems with decisions. Instead of allowing all possible second-stage decisions, the k-adaptability approach aims at calculating a limited set of k such decisions already in the first-stage before the uncertainty reveals. The parameter k can be adjusted to control the quality of the approximation. However, not much is known on how many solutions k are needed to achieve an optimal solution for the two-stage robust problem. In this talk we answer this question by deriving bounds on k for objective and constraint uncertainty. Furthermore, we derive approximation guarantees the k-adaptability approach provides for small values of k. The results give new insights on how many solutions are needed for problems as the decision dependent information discovery problem or the capital budgeting problem with constraint uncertainty.

Orateur: Jannis Kurtz (University of Amsterdam)

27 Iterated local search algorithms for adjustable robust optimization problems with discrete budget uncertainty

Two-stage robust optimization with integer recourse is a notoriously difficult class of problems, yet modelling many important applications. In this we talk, we discuss how to heuristically solve these problems, solving the adversarial problem and the outer minimization problem through local search algorithms. We focus on the case where all decision variables as well as the uncertainty are discrete sets. We compare numerically our algorithms with the recent exact algorithm recently proposed in the literature.

Orateur: Michael Poss (LIRMM, CNRS)

Mini-symposium: Communication-Efficient methods for distributed optimization and federated learning

Président de session: Laurent Condat (KAUST)

28 Communication-efficient distributed optimization algorithms

In distributed optimization and machine learning, a large number of machines perform computations in parallel and communicate back and forth with a server. In particular, in federated learning, the distributed training process is run on personal devices such as mobile phones. In this context, communication, that can be slow, costly and unreliable, forms the main bottleneck. To reduce communication, two strategies are popular: 1) local training, that consists in communicating less frequently; 2) compression. Also, a robust algorithm should allow for partial participation. I will present several randomized algorithms we developed recently, with proved convergence guarantees and accelerated complexity. Our most recent paper “LoCoDL: Communication-Efficient Distributed Learning with Local Training and Compression” has been presented at ICLR 2025 as a Spotlight.

Orateur: Dr Laurent Condat (KAUST)

29 Rethinking Optimality in Randomized Decentralized Optimization

We consider decentralized optimization over a network of $n$ workers, aiming to minimize
$$ f(x) = \frac{1}{n} \sum_{i=1}^n f_i(x), $$ where each $f_i$ is $\mu$-strongly convex and $L$-smooth. Most known convergence bounds rely on inner-outer loop structures that alternate synchronized gossip steps with (possibly randomized) local gradient updates, implicitly restricting the algorithm class to those with coordinated behavior. Recent work, such as DADAO (Nabli & Oyallon, ICML 2023), challenges this structure by introducing a fully stochastic scheme in which both communication and computation occur according to independent Poisson clocks. This eliminates the need for synchronization or gradient tracking and achieves communication-optimal convergence at a rate of $$ \mathcal{O} \left( n \cdot \frac{L}{\mu} \log \left( \frac{1}{\varepsilon} \right) \right), $$though this is not optimal in terms of total complexity. This raises an open question: Can we achieve the optimal convergence rate in decentralized settings by fully randomizing both communication and computation? The best known rate for such randomized, asynchronous (yet centralized) methods is $$ \mathcal{O} \left( \left( \sqrt{\frac{nL}{\mu}} + n \right) \log\left( \frac{1}{\varepsilon} \right) \right), $$ which outperforms known deterministic approaches in various regimes. However, current lower bounds are derived under structural assumptions that exclude such randomized schemes. This suggests a potential trade-off between achieving optimal communication complexity and optimal computation complexity.

This talk aims to expose this theoretical gap, revisit the assumptions underlying existing lower bounds, and discuss recent developments in randomized decentralized algorithms.

Orateur: Edouard Oyallon (CNRS, Sorbonne Universite)

30 Convergence and Linear Speed-Up in Stochastic Federated Learning

• Abstract: In federated learning, multiple users collaboratively train a machine learning model without sharing local data. To reduce communication, users perform multiple local stochastic gradient steps that are then aggregated by a central server. However, due to data heterogeneity, local training introduces bias. In this talk, I will present a novel interpretation of the Federated Averaging algorithm, establishing its convergence to a stationary distribution. By analyzing this distribution, we show that the bias consists of two components: one due to heterogeneity and another due to gradient stochasticity. I will then extend this analysis to the Scaffold algorithm, demonstrating that it effectively mitigates heterogeneity bias but not stochasticity bias. Finally, we show that both algorithms achieve linear speed-up in the number of agents, a key property in federated stochastic optimization.

Orateur: Paul Mangold (Univ. Lille, Inria, CNRS, Centrale Lille, UMR 9189 - CRIStAL, F-59000 Lille, France)

31 In-depth Analysis of Low-rank Matrix Factorisation in a Federated Setting

We analyze a distributed algorithm to compute a low-rank matrix factorization on $N$ clients, each holding a local dataset $\mathbf{S}^i \in \mathbb{R}^{n_i \times d}$, mathematically, we seek to solve $min_{\mathbf{U}^i \in \mathbb{R}^{n_i\times r}, \mathbf{V}\in \mathbb{R}^{d \times r} } \frac{1}{2} \sum_{i=1}^N \|\mathbf{S}^i - \mathbf{U}^i \mathbf{V}^\top\|^2_{\text{F}}$. Considering a power initialization of $\mathbf{V}$, we rewrite the previous smooth non-convex problem into a smooth strongly-convex problem that we solve using a parallel Nesterov gradient descent potentially requiring a single step of communication at the initialization step. For any client $i$ in $\{1, \dots, N\}$, we obtain a global $\mathbf{V}$ in $\mathbb{R}^{d \times r}$ common to all clients and a local variable $\mathbf{U}^i$ in $\mathbb{R}^{n_i \times r}$. We provide a linear rate of convergence of the excess loss which depends on $\sigma_{\max} / \sigma_{r}$, where $\sigma_{r}$ is the $r^{\mathrm{th}}$ singular value of the concatenation $\mathbf{S}$ of the matrices $(\mathbf{S}^i)_{i=1}^N$. This result improves the rates of convergence given in the literature, which depend on $\sigma_{\max}^2 / \sigma_{\min}^2$. We provide an upper bound on the Frobenius-norm error of reconstruction under the power initialization strategy. We complete our analysis with experiments on both synthetic and real data.

Orateur: Constantin Philippenko (Inria Paris)

16:00 Coffee break

Stochastic Programming: Computational Methods For Stochastic Optimization

Président de session: Robert Bassett (Naval Postgraduate School)

32 Backward-Forward-Backward Splitting of the Relaxed Multi-Stage Stochastic Weapon Target Assignment Problem

We apply the recently proposed Coupled Adaptable Backward-Forward-Backward Resolvent Splitting Algorithm (CABRA) to the continuous relaxation of the multi-stage stochastic weapon target assignment problem. Our formulation allows decentralized optimization across weapon platforms with minimal data exchange requirements. The CABRA formulation also allows us to adapt the splitting structure to match the available communication paths between weapon platforms, relying on direct connectivity only between platforms which share a target. Unlike other recently developed adaptable forward backward methods, CABRA takes direct advantage of the structure of the nonanticipativity constraints in the lifted problem, thereby reducing memory requirements and accelerating convergence. We demonstrate this in a set numerical experiments which validate the performance of the formulation.

Orateur: Peter Barkley (Naval Postgraduate School)

33 Solving Stochastic Programs with GPUs: A Literature Review

We present a computational study exploring methods for solving Stochastic Linear Programs (SLPs) on Graphics Processing Units (GPUs). We examine the operator splitting approach of O’Donoghue et al. and the Primal Dual Hybrid Gradient method of Chambolle and Pock, with the aim of specializing both to exploit the unique sparse structures inherent in SLPs. Our work focuses on adapting these methods to enhance computational efficiency and scalability for large-scale problems.

Orateur: Larry Wigington (Naval Postgraduate School)

34 An Introduction to Matrix Parametrized Proximal Splitting

In this talk we introduce the Matrix Parametrized Proximal Splitting, a proximal splitting method which generalizes a number of splitting methods introduced in the recent literature. Our formulation is capable of constructing convergent splitting algorithms for arbitrary communication constraints imposed between the proximal operators. We review central aspects of the method, state requirements for convergence, and then discuss computational performance.

Orateur: Robert Bassett (Naval Postgraduate School)

35 An Enhanced Learning-to-Optimize Framework for the Stochastic Inventory Routing Problem

The integration of inventory management and vehicle routing decisions creates a complex combinatorial optimization problem, known as the Inventory Routing Problem (IRP), which is a fundamental challenge in supply chain optimization and has been widely studied over the past decades. However, in the Stochastic IRP (SIRP), where retailer demand varies over time, the problem becomes more challenging. This paper focuses on the SIRP where the demand distribution is unknown in advance, stockouts are allowed during the planning horizon without back-ordering, and vehicle capacity is limited. To address this challenge, we propose an Enhanced Learning to Optimize (E-L2O) pipeline, jointly optimizing replenishment and routing decisions. The multi-stage SIRP is decomposed into a per-period solving process, leveraging the predictive and statistical capabilities of neural networks to incorporate future stochastic variables and related factors into current decisions. To enable more flexible replenishment strategies, we introduce an enhanced Fenchel-Young loss function to guide both replenishment and routing decisions. Through extensive computational experiments, we demonstrate that the resulting algorithm achieves solutions of unmatched quality to date, especially on large-scale benchmark instances.

Orateur: Jingyi Zhao

(Distributionally) Robust Optimization: Exploring Structural Perspectives in Distributionally Robust Optimization

Président de session: Yiling Zhang

36 Intuitive and Fast Algorithms for Two-Stage Distributionally Robust Optimization

Distributionally robust optimization (DRO) has been recognized as a powerful optimization scheme to handle random factors in decision making. The mainstream solution methods are generally based on duality theory, which might be technically challenging and less intuitive. In this talk, we consider two-stage DRO from the primal perspective, and develop a corresponding decomposition algorithm (and its variants). It is easy to implement and also demonstrates a strong capacity in computing two-stage DRO.

Orateur: Bo Zeng (University of Pittsburgh)

37 A Primal Perspective on Distributionally Robust Two-Stage Problems with Integer Recourse

In this talk, we introduce and study a two-stage distributionally two-stage linear problem with integer recourse, where the objective coefficients are random. The random parameters follow the worst-case distribution belonging to a second-order conic representable ambiguity set of probability distributions. We show that the worst-case recourse objective, under various risk measures, can be formulated as a conic program from a primal perspective. This method also provides additional information on the probability of attaining an integer recourse solution, extending the concept of persistency studied in Bertsimas et al. (2006). Unlike the marginal moment sets used in Bertsimas et al. 2006), the second-order conic representable ambiguity sets in our method offer greater flexibility by incorporating more distributional information.

Orateur: Yiling Zhang

38 Distributionally robust optimization through the lens of submodularity

Distributionally robust optimization is used to solve decision making problems under uncertainty where the distribution of the uncertain data is itself ambiguous. While several tractable models have been proposed for continuous uncertainty using a convex ambiguity set, fewer results are known for discrete uncertainty. In this work, we identify a class of distributionally robust optimization problems with discrete uncertainty that are solvable in polynomial time by viewing it through the lens of submodularity. Towards this, we define a submodular ambiguity set which specifies upper bounds on the expected values of a finite set of submodular functions of the random vector. With univariate and bivariate discrete random variables, we develop a polynomial sized linear program to solve the problem of computing the sharpest upper bound on the expectation of the maximum of affine functions over this ambiguity set. We showcase the modeling power of the submodular ambiguity set by considering upper bounds on the Wasserstein distances between pairs of random variables while incorporating univariate marginal information and demonstrating the breadth of correlations that can be accommodated. Even with continuous uncertainty, this ambiguity set can incorporate information on the random variables that goes beyond existing models at the expense of implementing pseudo-polynomial time algorithms. Our results show that the submodular ambiguity set supplements the convex ambiguity set, both in terms of modeling and computation.

Orateur: Arjun Ramachandra

39 Solving two-stage distributionally robust optimization with mixed-integer ambiguity sets via a hybrid Benders and column-and-constraint decomposition method

We propose a decomposition algorithm to approximately solve two-stage distributionally robust optimization problems with mixed-integer ambiguity sets. Such settings are particularly relevant in non-cooperative contexts, such as unplanned disruptions or interdictions, where an adversary reacts to the defender's decisions. DRO is a natural fit, but resulting problems are difficult to reformulate as solvable MILPs unless the ambiguity set follows a specific structure. Therefore, we propose a data-driven approach to find an upper bound to the original problem. The ambiguity set is split into integer and continuous sets, so that the recourse model is easily reformulated into a tractable form by relying on known strong duality results. The resulting problem is solved using a traditional decomposition approach combining Benders’ decomposition and column-and-constraint generation. We demonstrate our approach on a network design problem with interdiction constraints.

Orateur: Pascal Quach (CentraleSupelec)

pascal_quach_icsp_2025.pdf

Application in energy, finance or logistics: Applications of Stochastic Programming in Disaster Relief and Resilience

Président de session: Yongjia Song (Clemson University)

40 Mean-Risk Stochastic Integer Programming with Endogenous Uncertainty: Modeling and Application to Wildfire Management

Two-stage mean-risk stochastic integer programming (MR-SIP) with endogenous uncertainty involves here-and-now decisions that influence future outcomes and is very challenging to solve. We derive a decomposition method for this class of MR-SIP and apply it to an important problem in wildfire management, namely optimal fuel treatment planning (FTP) under uncertainty. The uncertainty stems from fuels (vegetation), fire occurrence, and fire behavior. Fuel treatment methods such as prescribed burning and mechanical thinning are aimed at reducing hazardous fuels and thus, influence the uncertainty. Consequently, FTP involving multiple treatment types and areas to treat to minimize wildfire risk is very challenging. In this work, we devise a novel MR-SIP FTP model that integrates fuel treatment and firefighting resource deployment planning before fires happen, which are typically done separately. The new model uses the expected excess risk measure, which given a target level of wildfire damage cost, minimizes the mean excess above the target level. We parameterize the FTP model through standard wildfire behavior simulation software in generating scenarios and apply it in a case study to historical wildfire data for a study area in West Texas, U.S.A. The study provides several practical insights for FTP decision-making.

Orateur: Dr Lewis Ntaimo (Texas A&M University)

41 Dynamic Transmission Line switching amidst decision-dependent wildfire-prone conditions

During dry and windy seasons, environmental conditions significantly increase the risk of wildfires, exposing power grids to disruptions caused by transmission line failures. Wildfire propagation exacerbates grid vulnerability, potentially leading to prolonged power outages. To address this challenge, we propose a multi-stage stochastic optimization model that dynamically adjusts transmission grid topology in response to wildfire propagation. By accounting for decision-dependent uncertainty, where line survival probabilities depend on usage, we employ distributionally robust optimization to model uncertainty in line survival distributions, aiming to develop an optimal response policy. We adapt the stochastic nested decomposition algorithm and derive a deterministic upper bound for its finite convergence. Using realistic data from the California transmission grid, we demonstrate the superior performance of the dynamic response policies against two-stage alternatives through a comprehensive case study. In addition, we construct easy-to-implement policies that significantly reduce computational burden while maintaining good performance in real-time deployment.

Orateur: Juan-Alberto Estrada-Garcia (University of Michigan)

42 Multistage Stochastic Programming for Hurricane Relief Logistics Planning with Rolling Forecast Uncertainty

In this talk, we will discuss multi-stage stochastic programming (MSP) models and solution approaches for humanitarian relief logistics planning in hurricane disasters. Specifically, we study how the rolling forecast information can be integrated in an MSP model via the Martingale Model of Forecast Evolution (MMFE) to provide optimal adaptive logistics decision policies. We investigate state-space modeling to address the high-dimensional state space as a result of the MMFE model. Our numerical results and sensitivity analyses demonstrate the value of MSP for hurricane relief logistics planning compared to approaches that utilize rolling forecast information in a rolling-horizon fashion. We also investigate various trade-offs between policy flexibility, solution quality, and computational effort, from which we gain valuable managerial insights for the practitioners.

Orateur: Yongjia Song (Clemson University)

Chance-constrained programming: Contributed talks

Président de session: Welington de Oliveira (Mines Paris PSL)

43 A Chance-Constrained Programming Approach to Wavelength Dimensioning Under Traffic Uncertainty

We consider the wavelength dimensioning problem in wavelength division multiplexing optical networks, which aims to determine the set of wavelengths assigned to each link to accommodate future connection requests under uncertain traffic conditions. To tackle this, we propose a two-stage chance-constrained mixed-integer programming (2S-CCMIP) model that minimizes the total assigned wavelength capacity while ensuring (in the second stage, via a proper routing and wavelength assignment model) operational performance requirements are met with high probability, based on a given risk tolerance. To achieve reductions in the allocated wavelength capacity while accommodating heterogeneous traffic densities across the network, we use a non-uniform dimensioning strategy that allows different links to have different set of assigned wavelengths. For solving the 2S-CCMIP model, we develop a tailored branch-and-cut algorithm, incorporating problem-specific cutting planes. We also design a novel heuristic method that generates feasible solutions from any infeasible integer solution. We propose a two-phase framework that effectively integrates the proposed enhancements. Through numerical experiments on three real-world network topologies, we demonstrate the effectiveness of our method in reducing wavelength capacity and improving computational efficiency compared to existing alternatives.

Orateur: Haoyuan Xue (University of Toronto)

wavelength dimensioning ccp.pptx

44 Nonlinear cuts for chance-constrained problems with right-hand side uncertainty

In this talk, we address joint chance-constrained optimization problems where the only uncertain parameter is the right-hand side coefficients in an inequality system. By leveraging one-dimensional marginals, we construct nonlinear cuts that accurately approximate the probability function, which need not be differentiable or satisfy generalized concavity properties. These cuts are integrated into a proximal-like algorithm, defining iterates as stationary points of a nonlinear master program that can be solved using standard nonlinear programming solvers. Numerical experiments demonstrate the potential of our approach compared to traditional techniques that employ (sub)gradient linearizations.

Orateur: Welington de Oliveira (Mines Paris PSL)

45 Chance-Constrained Optimization with Complex Variables

Optimization problems involving complex variables, when solved, are typically transformed into real variables, often at the expense of convergence rate and interpretability. In this work, we introduce a novel formalism for a prominent problem in stochastic optimization involving complex random variables, which is termed the Complex Chance-Constrained Problem (CCCP). The study specifically examines the linear CCCP under complex normal distributions for two scenarios: one with individual probabilistic constraints and the other with joint probabilistic constraints. For the individual case, the core methodology reformulates the CCCP into a deterministic Second-Order Cone Programming (SOCP) problem, ensuring equivalence to the original CCCP. For the joint case, an approximation is achieved by deriving suitable upper and lower bounds, which also leads to a SOCP formulation. Finally, numerical experiments on a signal processing application—specifically, the Minimum Variance Beamforming problem with mismatch using MVDR—demonstrate that the proposed formalism outperforms existing approaches in the literature. A comparative analysis between the joint and individual CCCP cases is also included.

Orateur: Mme Raneem Madani (Laboratoire Des Signaux Et Systèmes, L2s - Centralesupélec)

46 A continuous-time optimal control approach based on Pontryagin's maximum principle with chance constraints

In this talk, we present a general method for solving the optimal control problem of trajectory planning for autonomous vehicles in continuous time with robustness to uncertainty. In a precedent work [1], we proposed a formulation as a non-linear optimisation problem with an integral cost function including chance constraints. Our present work uses Pontryagin's maximum principle to solve autonomous vehicles' reference trajectory planning problem in continuous-time. We obtain a system of ordinary differential equations (ODE) equivalent to minimising an objective function under constraints preserving the continuous-time formulation. We include the chance constraints in the system thanks to their deterministic equivalent formulation as a second-order conic programming problem [2] [3].

Let $\mathbf{z} \in \mathcal{Z}, \mathbf{u} \in \mathcal{U}$ be the state and control under constraints, respectively. For $t \in \mathbb{R}$ and $n, m \in \mathbb{N}$, let $z(t) \in \mathbb{R}^n$ and $u(t) \in \mathbb{R}^m$. We have $\mathbf{z} = (z(t))_{t \in [0, t_f]}$ and $\mathbf{u} = (u(t))_{t \in [0, t_f]}$. The integral cost function to minimise is $J = \int^{t_f}_0 l(z(t), u(t))dt$ with $l(z(t), u(t)): \mathbb{R}^n \times \mathbb{R}^m \longmapsto \mathbb{R}$ the integrand and $t_f \in \mathbb{R}^+_*$ the final time. We denote $\frac{dz(t)}{dt} = f(z(t), u(t))$ with $f(z(t), u(t)): \mathbb{R}^n \times \mathbb{R}^m \longmapsto \mathbb{R}^n$ the system dynamics and $\lambda(t) \in \mathbb{R}^n$ the costates associated with $z(t)$.

For $k \in \mathbb{N}$, we denote $S(z(t)) \in \mathbb{R}^k$ the deterministic equivalent formulation of the chance constraints over the state vector $z(t)$ [4]. Let $q \in \mathbb{N}$ the order of temporal derivative such that $\frac{d^qS(z(t))}{dt^q}$ depends explicitly on the state $z(t)$ and the command $u(t)$ i.e there exists a function $g(z(t), u(t)): \mathbb{R}^n \times \mathbb{R}^m \longmapsto \mathbb{R}^k$ such as $\frac{d^qS(z(t))}{dt^q} = g(z(t), u(t))$. We include this term in the Hamiltonian with time-dependent Lagrange multipliers $\eta(t) \geq 0$. The Hamiltonian is then given by:

\begin{align}
H(z(t),u(t),\lambda(t), \eta(t)) = l(z(t),u(t)) + \lambda^T(t) f(z(t), u(t)) + \eta^T(t) \frac{d^qS(z(t))}{dt^q}
\end{align}

By applying Maximum Principle, we derive a two-point boundary value problem (TPBVP), which can be solved as an optimisation problem of finding the values for the costates at initial time, denoted $\lambda(0) \in \mathbb{R}^n$ [5]. To initialise the algorithm, we will use the solution from direct methods optimisation approach, for the discrete model, from our previous work [1].
We will evaluate the proposed approach based on numerical simulations of real scenarios from industrial applications of autonomous vehicle trajectories, highlighting its efficiency.

References
[1] A. Valli, S. Zhang, and A. Lisser, Continuous-time optimal control for trajectory planning under uncertainty. International Journal of Vehicle Autonomous Systems, 1 . doi:10.1504/IJVAS.2025.10072190.
[2] S. Kataoka, A Stochastic Programming Model, Econometrica, vol. 31, n°1/2, p. 181‑196, 1963, doi: 10.2307/1910956.
[3] C. van de Panne et W. Popp, Minimum-Cost Cattle Feed under Probabilistic Protein Constraints, Management Science, vol. 9, n°3, p. 405‑430, 1963.
[4] A. Prékopa, Stochastic Programming. Dordrecht: Springer Netherlands, 1995. doi: 10.1007/978-94-017-3087-7.
[5] A. E. Bryson, Applied Optimal Control: Optimization, Estimation and Control. New York: Routledge, 2018. doi: 10.1201/9781315137667.

Orateur: M. Ange Valli (Laboratoire des Signaux et Systèmes (L2S), Université Paris-Saclay, CNRS, CentraleSupélec)

Presentation_Ange_Valli_ICSP.pdf

ML: Contributed talks

Président de session: Vladimir Norkin (V.M.Glushkov Institute of Cybernetics)

47 It's All in the Mix: Wasserstein Classification and Regression with Mixed Features

Problem definition: A key challenge in supervised learning is data scarcity, which can cause prediction models to overfit to the training data and perform poorly out of sample. A contemporary approach to combat overfitting is offered by distributionally robust problem formulations that consider all data-generating distributions close to the empirical distribution derived from historical samples, where 'closeness' is determined by the Wasserstein distance. While such formulations show significant promise in prediction tasks where all input features are continuous, they scale exponentially when discrete features are present.

Methodology/results: We demonstrate that distributionally robust mixed-feature classification and regression problems can indeed be solved in polynomial time. Our proof relies on classical ellipsoid method-based solution schemes that do not scale well in practice. To overcome this limitation, we develop a practically efficient (yet, in the worst case, exponential time) cutting plane-based algorithm that admits a polynomial time separation oracle, despite the presence of exponentially many constraints. We compare our method against alternative techniques both theoretically and empirically on standard benchmark instances.
Managerial implications: Data-driven operations management problems often involve prediction models with discrete features. We develop and analyze distributionally robust prediction models that faithfully account for the presence of discrete features, and we demonstrate that our models can significantly outperform existing methods that are agnostic to the presence of discrete features, both theoretically and on standard benchmark instances.

Orateur: Mohammad Reza Belbasi (Imperial College Business School)

48 On the Computation of General Constrained Wasserstein Barycenters

This work explores constrained Wasserstein barycenters (CWB), extending the applicability of the classical Wasserstein barycenter (WB) to pre-required geometric, statistical, or constraints. While the WB problem has been extensively studied, constrained settings pose significant challenges, particularly for nonconvex constraint sets. Building upon the Method of Averaged Marginals (MAM), we propose two different algorithms with convergence guarantees and a promising heuristic method.
We first extend MAM to solve the CWB problem for convexly constrained sets, providing rigorous mathematical guarantees for exact convergence. For nonconvex constraint sets, we develop a heuristic extension of MAM, and incorporating a Difference-of-Convex (DC) model and progressive decoupling methods we ensure convergence to critical points. Finally, we evaluate the numerical performance of these methods on diverse applications, demonstrating both the computational efficiency and practical relevance of CWBs.

Orateur: Gregorio Martinez Sempere (Minesparis-psl)

49 On adaptive kernel learning

The study proposes and explores a wide area of application of machine learning methods in applied mathematics, namely, parametric analysis of mathematical models by machine learning methods, in particular, by adaptive kernel support vector machines. The kernel support vector machine is extended by the ability to use a continuum (multivariate parametric) family of kernels to approximate the dependence under study. For example, it is proposed to use variable width kernels and variable anisotropic kernels to reduce the approximation error. Thus the standard for kernel learning Reproducing Kernel Hilbert Space is replaced by a much broader kernel subspace of square integrable functions. While kernels in RKHS act on functions (via the inner product) as Dirac’s delta-function, kernels in L_2 act on functions as smoothing/mollifying operators. An essential problem in machine learning is selecting regularization, in particular the scale of the regularization parameter. In the paper, we select the regularization parameter by minimization of the approximation error on training and/or test data. To train the adaptive support vector machine, it is proposed to use a combination of traditional kernel weights optimization methods (quadratic as in SVM) and global optimization methods to optimize kernel parameters.

Orateur: Vladimir Norkin (V.M.Glushkov Institute of Cybernetics)

50 Generalized Naive Bayes with continuous explanatory variables

Naive Bayes is one of the most widely used machine learning algorithms, appreciated for its simplicity, efficiency, and ease of interpretation—qualities that make it appealing across various fields. However, Naive Bayes operates under the assumption that the explanatory variables are conditionally independent given the class label, an assumption that often does not hold true in practice.

To address this limitation, we propose a method that relaxes the independence assumption by allowing certain dependencies between the explanatory variables. The central idea of our approach is to find a structure that best approximates the joint probability distribution of the data while minimizing the Kullback-Leibler divergence. We introduce a greedy algorithm that gradually builds this structure step by step.

Initially, the algorithm was designed for cases with discrete variables. We are now adapting it for situations where the explanatory variables follow a joint multivariate Gaussian probability distribution. Furthermore, we extend our approach to accommodate more general continuous variables.

Finally, we evaluate the performance of our method against other classification techniques using real-world datasets. Our method is also capable of identifying the most informative set of explanatory variables.

Orateur: Edith Alice Kovács (Budapest University of Technology and Economics)

Sequential decision-making under uncertainty: Contributed talks

Président de session: Jingui Xie (Technical University of Munich)

51 Multi-Stage Disaster Response and Platelet Resource Allocation: A Stochastic Dual Dynamic Programming Approach

In this paper, we study the stochastic casualty response planning problem and propose a multi-stage stochastic programming model, where initial decisions—such as the location of alternative care facilities (ACFs) and rescue vehicle assignments—are fixed, while patient assignments and allocations of apheresis machines (AM) for blood extraction are updated dynamically as uncertainty unfolds. In this framework, patient demands, blood donor availability, and hospital treatment capacities are treated as uncertain parameters. Our model focuses on deploying newly introduced portable AMs, like the Trima Accel 7, and incorporates both apheresis blood donation and whole blood collection methods, along with platelet transshipments among medical facilities to meet varying demands. This approach aims to improve patient outcomes by optimizing three key performance indicators: timely transport from disaster areas to medical facilities, timely surgeries, and compatible platelet transfusions. By matching platelet age and blood type to injury severity, we reduce the risks associated with mismatched transfusions. To address the scalability challenges in multistage stochastic optimization, we employ stochastic dual dynamic programming (SDDP) and benchmark it against nested Benders decomposition (NBD). To further enhance the efficiency of these algorithms, we develop a wide range of acceleration techniques, including strong cuts, multiple cuts, lower bounding functional valid inequalities (LBFVIs), and warm-up strategies. Effective scenario sampling is achieved through randomized quasi-Monte Carlo (RQMC), while K-means++ clustering is applied for scenario reduction, decreasing the number of scenarios by several orders of magnitude. We carry out extensive computational experiments demonstrating that these enhancements significantly boost the performance of the SDDP algorithm, resulting in a 6,078% reduction in the objective function across 2,500 out-of-sample scenarios and a 40% improvement in the value of the stochastic solution. Finally, a case study from the 2011 Van earthquake in Turkey demonstrates the practical applicability and efficiency of our optimized approach.

Orateur: Pedram Farghadani Chaharsooghi (Concordia University)

52 Risk-Averse Treatment Allocation in Clinical Trials: A Multiarmed Bandit Design

Multiarmed bandit problems (MABs) present a class of optimal control problems well-suited for modeling resource allocation under uncertainty. This study explores the application of MABs in the context of clinical trial design. While traditional risk-neutral MABs aim to maximize the expected total number of effective treatments, this study considers the limitations of this objective, as treatments that perform well on average may exhibit significant variability and adverse effects for certain patients. To address this, a novel risk-averse MAB approach using dynamic risk measures is introduced for treatment allocation, employing a Bayesian Bernoulli model. The performance of this approach is evaluated against other allocation rules, including fixed randomization. The findings shed light on the benefits of incorporating risk-averse strategies in clinical trial designs, offering insights for more effective and patient-centric decision-making.

Orateur: Dr Ozlem Cavus (Associate Professor)

53 Universal Lung Cancer Screening Guidelines Under Heterogeneous Patient Responses

Health organizations (society) prefer to recommend universal screening guidelines to at-risk individuals (patients) for various diseases, with coverage typically provided by third-party payers. However, patients are heterogeneous both in disease risk and disutility associated with screening, resulting in varying health outcomes. Infrequent recommendations leave at-risk patients to decide if to pay out-of-pocket in the interim, while frequent recommendations may result in unnecessary screening disutility for low-risk patients and unnecessary costs to society. Moreover, patient adherence to guidelines remains low for many diseases, further complicating the health benefits and costs realized in practice. We address these challenges in the context of lung cancer screening for eligible ever-smokers and employ a bilevel optimization model to compute universal lung cancer screening guidelines that maximize the societal net monetary benefit (NMB). With society (leader) determining the covered universal screening schedule, representative patient classes (followers) are modeled as partially observable Markov decision processes (POMDPs), maximizing their own NMB with respect to their smoking level, screening disutility, willingness-to-pay for out-of-pocket costs, and adherence rate. We employ a grid-based approximation scheme to embed the follower problems within a mixed-integer bilevel program.

Orateur: Raul Garcia (Rice University)

54 Mitigating Risks in Critical Care with Analytics

Deciding when to stop medical treatment with uncertain outcomes and predictions is a critical challenge in intensive care units. This research develops a risk-sensitive approach to optimal medical stopping decisions by integrating outcome variability into the decision-making process and incorporating predictive information about the next state. We model the problem using a risk-sensitive Markov decision process with an entropic risk measure to capture decision risk. Our analysis reveals that under some assumptions the optimal policy follows a threshold-based structure, with a submodular value function and a risk-aware decision framework. We identify three distinct risk-sensitive strategies that diverge from the nominal stopping problem: an aggressive policy under deterministic terminal costs, a conservative policy, and a mixed strategy that transitions from conservative to aggressive actions. To evaluate the effectiveness of our model, we conduct numerical experiments on two critical decision cases: extubation and discharge. Our results demonstrate that the proposed approach achieves a more favorable balance between expected costs and risk exposure—where a slight increase in expected cost can lead to a substantial reduction in risk. These findings underscore the inherent trade-off between the immediate risks of stopping treatment and the ongoing risks of continued treatment. By leveraging our model, healthcare managers can significantly mitigate downside risk with a minimal increase in expected costs, enhancing decision-making in high-stakes clinical settings.

Orateur: Jingui Xie (Technical University of Munich)

Mini-symposium: Models and Methods for Stochastic Non-Convex Optimization and Equilibrium Problems

Président de session: Miguel Lejeune (George Washington University)

55 Using a difference-of-convex (DC) functions approach to solving stochastic mixed complementarity problems with chance constraints for the players.

We present both the DC algorithm as well as several examples in chance-
constrained programming as well as other deterministic applications to showcase the
applicability and success of this new approach. In particular this approach has been successfully applied to solving many deterministic and stochastic mixed complementarity problems (MCPs). MCPs generalize non-cooperative games, the KKT conditions of optimization problems, and many more applications in engineering and economics. See [1] for more details.
[1] Gabriel, S.A., Conejo, A.J., Fuller, J.D., Hobbs, B.F. and Ruiz, C., 2012. Complementarity modeling in energy markets (Vol. 180). Springer Science & Business Media.

Orateur: Prof. STEVEN GABRIEL (University of Maryland/NTNU/Aalto University)

56 Bi-Parameterized Two-Stage Stochastic Min-Max and Min-Min Mixed Integer Programs

We introduce two-stage stochastic min-max and min-min integer programs with bi-parameterized recourse (BTSPs), where the first-stage decisions affect both the objective function and the feasible region of the second-stage problem. To solve these programs efficiently, we introduce Lagrangian-integrated L-shaped ($L^2$) methods, which guarantee exact solutions when the first-stage decisions are pure binary. For mixed-binary first-stage programs, we present a regularization-augmented variant of this method. We also introduce distributionally robust bi-parameterized two-stage stochastic integer programs and present an extension of the $L^2$ method and a reformulation-based method for programs with finite and continuous supports, respectively. Our computational results show that the $L^2$ method surpasses the benchmark method for bi-parameterized stochastic network interdiction problems, solving all instances in 23 seconds on average, whereas the benchmark method failed to solve any instance within 3600 seconds. Additionally, it achieves optimal solutions up to 18.4 and 1.7 times faster for instances of risk-neutral and distributionally robust bi-parameterized stochastic facility location problems, respectively. Furthermore, BTSPs have applications in solving stochastic problems with decision-dependent probability distributions or sets of distributions (ambiguity set). The $L^2$ method outperforms existing approaches, achieving optimal solutions 5.3 times faster for distributionally robust facility location problem with a decision-dependent and non-relatively complete ambiguity set.

Orateur: Manish Bansal (Virginia Tech)

57 Capacity investment decisions in equilibrium: a distributionally robust approach

In electricity systems, investment in generation capacity is subject to risk. The distribution of uncertain parameters on which investment decisions depend might not be fully observed in historical values. In Europe, this was recently illustrated by the crisis of exceptionally high power prices during the 2021-2023 period, which was subsequently followed by a regime of extremely low and even negative prices. In that vein, ambiguity aversion reflects a lack of confidence in the distribution of uncertainty, while risk aversion is concerned with realizations of uncertainty. We study a competitive market with investors who are averse to ambiguity. Such a market is represented as an equilibrium model, where each agent solves a Wasserstein distributionally robust optimization problem regarding its investment decisions. Investments could be hedged by contracts. We derive a convex reformulation of the problem, demonstrate the existence of equilibria, and prove a version of the welfare theorem in this ambiguous context. Via simulations, we find that, as with risk aversion, ambiguity aversion results in capacity-investment deferrals. We show however that, unlike standard results obtained with risk-aversion models, ambiguity cannot be hedged through financial contracts when their revenues are indexed on spot prices. Finally, we highlight that state-backed support schemes such as Contracts for Difference are welfare-improving and capacity-preserving under ambiguity.

Orateur: Julien Ancel (Laboratoire de Génie Industriel, Centralesupélec, Université Paris-Sacaly)

58 Dynamic Operational Planning in Warfare: A Stochastic Game Approach to Military Campaigns

We study a two-player discounted zero-sum stochastic game model for dynamic operational planning in military campaigns. At each stage, the players manage multiple commanders who order military actions on objectives that have an open line of control. When a battle over the control of an objective occurs, its stochastic outcome depends on the actions and the enabling support provided by the control of other objectives. Each player aims to maximize the cumulative number of objectives they control, weighted by their criticality. To solve this large-scale stochastic game, we derive properties of its Markov perfect equilibria by leveraging the logistics and military operational command and control structure. We show the consequential isotonicity of the optimal value function with respect to the partially ordered state space, which in turn leads to a significant reduction of the state and action spaces. We also accelerate Shapley’s value iteration algorithm by eliminating dominated actions and investigating pure equilibria of the matrix game solved at each iteration. We demonstrate the computational value of our equilibrium results on a case study that reflects representative operational-level military campaigns with geopolitical implications. Our analysis reveals a complex interplay between the game’s parameters and dynamics in equilibrium, resulting in new military insights for campaign analysts.

Orateur: Mathieu Dahan (Georgia Institute of Technology)

Mini-symposium: Robust Optimization and Machine Learning

Président de session: Aras Selvi (Imperial College London)

59 Learning Data-Driven Uncertainty Sets via Mean Robust Optimization

Robust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions when pessimistic assumptions are made on the uncertain parameters. Wasserstein distributionally robust optimization can reduce conservatism by being data-driven, but it often leads to large problems with prohibitive solution times. In this talk, we introduce Mean Robust Optimization, a general framework that combines the best of both worlds by constructing data-driven uncertainty sets based on compressed data, significantly improving computational tractability. By varying the number of clusters, Mean Robust Optimization balances computational complexity and conservatism, and effectively bridges robust and Wasserstein distributionally robust optimization. We show finite-sample performance guarantees and explicitly control the potential pessimism introduced by any clustering procedure. We further extend Mean Robust Optimization to sequential decision problems with streaming data, by dynamically updating the clusters to efficiently adjust the uncertainty sets. We illustrate the benefits of our framework on several numerical examples, obtaining significant computational speedups with little-to-no effect on the solution quality.

Orateur: Bartolomeo Stellato (Princeton University)

60 Tractable Robust Markov Decision Processes

In this talk we investigate the tractability of robust Markov Decision Processes (RMDPs) under various structural assumptions on the uncertainty set. Surprisingly, we show that in all generality (i.e. without any assumption on the instantaneous rewards), s-rectangular and sa-rectangular uncertainty sets are the only models of uncertainty that are tractable. Our analysis also shows that existing non-rectangular models, including r-rectangular uncertainty and new generalizations, are only weakly tractable. in that they require an additional structural assumption that the instantaneous rewards do not depend on the next state, and in this case they are equivalent to rectangular models, which severely undermines their significance and usefulness. Interestingly, our proof techniques rely on identifying a novel simultaneous solvability property, which we show is at the heart of several important properties of RMDPs, including the existence of stationary optimal policies and dynamic programming-based formulations. The simultaneous solvability property enables a unified approach to studying the tractability of all existing models of uncertainty, rectangular and non-rectangular alike.

Orateur: M. Julien Grand-Clément (HEC Paris)

61 Rectangularity and duality of distributionally robust Markov decision processes

The main goal of this talk is to discuss several approaches to formulation of distributionally robust counterparts of Markov decision processes, where the transition kernels are not specified exactly but rather are assumed to be elements of the corresponding ambiguity sets. The intent is to clarify some connections between the game and static formulations of distributionally robust MDPs, and delineate the role of rectangularity associated with ambiguity sets in determining these connections. As some applications, implications on the strong duality, existence of nonrandomized optimal policies, and new ambiguity set for the static formulation will be discussed.

Orateur: Yan Li (Texas A&M University)

62 Room for Improvement: Optimal and Fair Housing Allocation via Weakly Coupled Markov Decision Processes

Motivated by a housing allocation problem faced by our public-sector partner, the Los Angeles Homeless Services Authority (LAHSA), we study sequential resource allocation in high-stakes social settings, where fairness is critical. Each month, we must allocate limited housing capacity among individuals experiencing homelessness. We model this as a Markov Decision Process (MDP), where individuals transition between housing and homelessness states based on stochasticity. To manage complexity, we adopt a grouped weakly coupled MDP framework, clustering individuals by covariates (via robust ML techniques) and solving for an optimal policy using a fluid linear program. To enforce fairness, we introduce demographic parity constraints on both resource allocation and long-term outcomes across protected groups. By refining our clustering approach, we balance equity while maintaining distinctions based on other covariates. We also analyze the price of fairness, characterizing trade-offs between equity and housing stability. The resulting policies outperform historical allocations while mitigating disparities in access and outcomes.

Orateur: Aras Selvi (Imperial College London)

Cocktail

mar. 29 juillet

Plenary session: Alois Pichler

Président de session: Andrzej Ruszczynski (Rutgers University)

63 Quantization with Maximum Mean Discrepancies

We consider the distance of probability measures from varying angles. We discuss balanced and unbalanced transport, we consider entropic regularization and the maximum mean discrepancy distance.
Quantization is the approximation of probability measures by simple and discrete measures. The quantization measures behave differently in these metrics – an aspect, which the talk addresses as well.

Orateur: Dr Alois Pichler (TU Chemnitz)

Slides

10:15 Coffee Break

Stochastic Programming: Applications of Stochastic Programming in Statistics and Risk Management

Présidents de session: Anton Malandii (Stony Brook University), Johannes Royset (University of Southern California)

64 Estimation of Conditional Distributions with Factor Model of Mixtures

This paper estimates distribution of a response variable conditioned on observing factors (features). We estimate the conditional quantile of the distribution as a mixture (weighted sum) of basis quantile functions with weights depending on factors. The suggested factor model has a closed-form expression. The calibration problem is reduced to conducting quantile regressions for all confidence levels simultaneously. However, the model does not suffer from ``quantile crossing'' by design. The calibration is equivalent to minimization of Continuous Probability Ranked Score (CRPS). We prove asymptotic normality of the estimator. The approach allows for application of neural networks for calibration of the model. Numerical experiments demonstrated high efficiency of the approach. In particular, we have used factor model of mixtures for predicting horse-racing outcomes.

Orateur: Stan URYASEV (Professor at Stony Brook University, USA)

65 Estimation of Conditional Mean of Distribution with Piecewise Linear Convex Optimization

Least-squares regression is typically formulated as a quadratic program. This talk presents a novel approach for reducing it to a piecewise linear convex minimization problem within the Risk Quadrangle Framework. Evidently, this problem can be reduced to linear programming. Crucially, this is not a heuristic step: the linearized formulation is statistically justified and shown to be equivalent to quantile regression, estimating the specific quantile corresponding to the mean. As a result, it inherits many benefits of quantile-based approaches, such as effective handling of heteroskedastic data and robustness to outliers.

Building on this result, we introduce two extensions: the expectile quadrangle and the biased mean quadrangle. While the expectile quadrangle is well-established in the literature, the biased mean quadrangle is a novel concept that offers new perspectives for risk management and regression analysis. In the biased mean quadrangle, the risk component can be applied in risk management, while the error component, referred to as the superexpectation error, can be used for biased mean regression.

We conduct extensive numerical experiments to justify our theoretical claims and highlight the computational benefits of our method. Our results highlight the versatility of the Risk Quadrangle Framework in unifying and extending classical regression methods, opening the door to broader applications and deeper theoretical understanding.

Orateur: Dr Terry Rockafellar

66 Risk-Adaptive Local Decision Rules

For parameterized mixed-binary optimization problems, we construct local decision rules that prescribe near-optimal courses of action across a set of parameter values. The decision rules stem from solving risk-adaptive training problems over classes of continuous, possibly nonlinear mappings. In asymptotic and nonasymptotic analysis, we establish that the decision rules prescribe near-optimal decisions locally for the actual problems, without relying on linearity, convexity, or smoothness. The development also accounts for practically important aspects such as inexact function evaluations, solution tolerances in training problems, regularization, and reformulations to solver-friendly models. The decision rules also furnish a means to carry out sensitivity and stability analysis for broad classes of parameterized optimization problems. We develop a decomposition algorithm for solving the resulting training problems and demonstrate its ability to generate quality decision rules on a nonlinear binary optimization model from search theory.

Orateur: Prof. Johannes Royset (University of Southern California)

67 Scalable Framework for Higher-Order Stochastic Dominance

Stochastic dominance is essential in decision-making under uncertainty and quantitative finance, providing a rigorous method for comparing random variables through their distribution functions.
Despite its importance in decision-making under uncertainty, (higher-order) stochastic dominance is computationally intractable due to infinitely many constraints.
Our research addresses this by reducing these constraints to a finite number, enabling algorithms that optimize returns while satisfying (higher-order) stochastic dominance conditions.
This contribution introduces StochasticDominance.jl, an open-source Julia package.
It is designed for verifying higher-order stochastic dominance between random variables and optimizing under higher-order stochastic dominance constraints.
As a black-box solution, it allows users to input data and obtain results seamlessly, making the analysis of higher-order stochastic dominance accessible with minimal technical expertise.

Orateur: Rajmadan Lakshmanan (Chemnitz University of Technology)

(Distributionally) Robust Optimization: Robust Inference and Learning: Advances in Theory and Applications

Président de session: Angelos Georghiou (University of Cyprus)

68 Robustness and Regret Tolerance

This paper shifts focus from the typical approach of maximizing expected reward to minimizing expected regret, aiming to find a solution whose expected reward is close to the oracle. While these two approaches are equivalent when the uncertainty distribution is given, they diverge when accounting for distributional ambiguity, which is characterized by the Wasserstein distance, for enhanced robustness. This can be achieved by requiring the decision maker to specify their tolerance for expected regret under the nominal distribution and minimize the excess regret beyond this threshold across any other distribution. By exploring the entire range of this threshold parameter, our regret-based model encompasses both empirical optimization and worst-case regret minimization, the latter of which is NP-hard. When the reward function is represented by a linear program (possibly involving recourse decisions, a random technology matrix, and a random right-hand side), we propose two tractable safe approximations that preserve feasibility and empirical consistency of the original problem. The first approximation is formulated as a robust linear program with convex uncertainty sets, while the second tightens and improves upon the first using positive semidefinite constraints. Finally, we demonstrate the advantages of our tolerance-oriented regret-based model over a similar target-oriented reward-based model and empirical optimization in the context of supply chain procurement and portfolio selection.

Orateur: Yilin Xue (National University of Singapore)

69 Can Inverse Optimization Compete with Neural Networks?

We study a class of learning models known as inverse optimization (IO), where the goal is to replicate the behaviors of a decision-maker (i.e., optimizer) with an unknown objective function. We discuss recent developments in IO concerning convex training losses and optimization algorithms. The main message of this talk is that IO is a rich learning model that can capture complex, potentially discontinuous behaviors, while the training phase is still a tractable convex program. We motivate the discussion with applications from control (learning the MPC control law), transportation (2021 Amazon Routing Problem Challenge), and robotics (comparing with state-of-the-art neural networks in MuJoCo environments).

Orateur: Peyman Mohajerin Esfahani (University of Toronto)

70 What’s hidden in the tails? Revealing and reducing optimistic bias in entropic risk estimation and optimization

The entropic risk measure is commonly used in high-stakes decision-making to account for tail risks. Empirical entropic risk estimator that replaces expectation in the entropic risk measure with sample average underestimates true risk. To correct this bias, a strongly asymptotically consistent bootstrapping procedure is proposed that fits a distribution to the data and then estimates the bias in the empirical estimator via bootstrapping. Two methods are proposed to fit a distribution to the data, a computationally intensive one that fits the distribution of empirical entropic risk, and a simpler one that fits the tail of the empirical distribution. The approach is applied to a distributionally robust entropic risk minimization problem with type-∞ Wasserstein ambiguity set, demonstrating improved calibration of size of the ambiguity set using debiased validation performance. In an insurance contract design problem, the proposed estimators reduce out-of-sample risk for insurers since they suggest more accurate premiums.

Orateur: Angelos Georghiou (University of Cyprus)

Application in energy, finance or logistics: Contributed talks

Président de session: Eduardo Moreno (Google Research)

71 Stochastic facility location problems with outsourcing costs

Stochastic facility location problems with outsourcing costs (SFLPOC) optimize facility placement and customer assignment under demand uncertainty. Excess demand beyond the capacity of a facility incurs outsourcing costs. This work addresses SFLPOC, aiming to minimize overall expected costs (placement, service and outsourcing). We model SFLPOC as a two-stage stochastic program. While prior work focused on specific assumptions or small scenario sets, we present methods suitable for general probability distributions. For discrete scenario sets, we improve upon classic Benders decomposition by exploiting the second-stage subproblem’s structure. To handle general distributions, we partition the probability space based on incumbent integer solutions. Coupled with Benders cuts, this provides an exact solution method for common distributions (e.g. Bernoulli, Exponential, Poisson, Gaussian). Additionally, we introduce a compact formulation specifically for i.i.d. demand distributions, allowing us to solve even continuous distribution problems to optimality. Computational experiments on established benchmarks demonstrate that our compact formulation consistently finds optimal solutions, while the Benders approach provides strong solutions with proven optimality gaps for general distributions, outperforming sample average approximations.

Orateur: Eduardo Moreno (Google Research)

72 Data-driven chance-constrained local electricity-hydrogen market under renewable generation uncertainty

In the context of the global transition towards net-zero emissions, local energy markets (LEMs) offer a practical and effective approach for integrating the increasing penetration of distributed energy resources, such as intermittent renewable generation, energy storage systems, and flexible loads. By facilitating active participation from small-scale consumers, producers, and prosumers in energy trading, LEMs enhance local energy balance and system efficiency. Moreover, clean energy carriers like hydrogen are being progressively incorporated into LEMs, driven by various government incentives and policy support. However, most existing research focuses predominantly on electricity trading, with limited attention to hydrogen and its associated market mechanisms. The development of integrated electricity-hydrogen markets remains insufficiently explored, particularly under uncertainty.
Therefore, we propose a novel multi-period coupled electricity-hydrogen local market framework that considers interactions on both the supply and demand sides—unlike the majority of existing studies which typically consider only single-sided energy management or isolate electricity and hydrogen markets. To capture renewable energy uncertainty, we propose a data-driven chance-constrained approach that leverages the advanced machine learning technique - normalizing flow, enabling representation of temporal correlations in renewable generation without relying on predefined distributional assumptions. Furthermore, we develop a decentralized market clearing mechanism based on a modified alternating direction method of multipliers with additional proximal terms, which guarantees convergence and optimality in theory even when the objective function lacks strongly convexity. Numerical simulations validate the effectiveness of the proposed approach, demonstrating a 17% reduction in total system costs compared to scenarios without local electricity trading.

Acknowledgements: Financial support from the EPSRC (under projects EP/T022930/1 and EP/W003317/1) is gratefully acknowledged.

Orateur: Xu Zhou (University College London)

73 Decomposition Strategies for Multi-Timescale Stochastic Optimization in Power System Applications

We propose decomposition algorithms to solve computationally challenging multi-timescale mixed-integer stochastic optimization problems in power system operation, where decisions across different time horizons are coordinated using aggregate state variables. Three distinct decomposition strategies are presented based on the stochastic model: (1) Price-directive decomposition for multi-horizon scenario trees; (2) Resource-directive decomposition for Markovian processes; and (3) A hybrid approach combining both price-directive and resource-directive decomposition. These methods allow coordination across timescales, improving system reliability and economic performance in applications like unit commitment. Furthermore, acknowledging that practical applications often involve solving sequences of similar problems, where achieving optimality for each instance is challenging, we introduce techniques that leverage computations from previous instances to progressively improve solution quality.

Orateur: Yihang Zhang (University of Southern California)

Application in energy, finance or logistics: Invited talk in Energy Applications

Présidents de session: Davi Valladão (PUC-Rio), Stein-Erik Fleten (Norwegian University of Science and Technology)

74 PolieDRO: a distributionally robust optimization framework for energy analytics

PolieDRO is a novel analytics framework for classification and regres-
sion that harnesses the power and flexibility of Data-Driven Distributionally Robust Optimization (DRO) to circumvent the need for regularization hyperparameters. Recent literature shows that traditional machine learning methods such as SVM and (square-root) LASSO can be written as Warserstein-based DRO problems. Inspired by those results we propose a hyperparameter-free ambiguity set that explores the polyhedral structure of data-driven convex hulls, generating computationally tractable regression and classification methods for any convex loss function.
We apply this novel framework to time series analysis tasks in the energy sector, with promising results.

Orateur: Tomás Gutierrez (Lamps Co)

75 Optimizing profile blocks for hydropower offers to the day-ahead market

We report on a two-phase optimization framework for combining short-term hydropower scheduling with offering into the European day-ahead electricity market. We use profiled block bids grouped in exclusive sets. The first phase solves a nonlinear deterministic model that generates a diverse and operationally feasible set of production blocks by accounting for startup costs, opportunity costs, and hydrological constraints. In the second phase, a two-stage stochastic program is used to select a subset of blocks for market submission under price uncertainty. The proposed approach captures a wide range of production scenarios while ensuring compliance with market design rules. By decomposing the problem and relaxing binary variables, the framework significantly reduces computational complexity and achieves fast solution times. Numerical experiments based on a real hydropower system demonstrate the model’s ability to produce effective bidding strategies, comparable to the hourly bidding methods.

Orateur: Stein-Erik Fleten (Norwegian University of Science and Technology)

Optimizing profile block bids in short-term hydropower scheduling: A two-phase model for the day-ahead market

76 Deviated Fixed-route Microtransit: Design and Operations

Microtransit offers opportunities to enhance urban mobility by combining the reliability of public transit and the flexibility of ride-sharing. This paper optimizes the design and operations of a deviated fixed-route microtransit system that relies on reference lines but can deviate on demand in response to passenger requests. We formulate a Microtransit Network Design (MiND) model via two-stage stochastic optimization, with a first-stage network design structure and a second-stage vehicle routing structure. We formulate the model with a tight second-stage relaxation thanks to a subpath-based representation of microtransit operations in a load-expanded network. We develop a double-decomposition algorithm combining Benders decomposition and subpath-based column generation. We prove that the algorithm maintains a valid optimality gap at each iteration and can converge to an optimal solution in a finite number of iterations. Using real-world data from Manhattan, results suggest that our method scales to large practical instances, with up to 10-100 candidate lines and hundreds of stops. Comparisons with transit and ride-sharing benchmarks suggest that microtransit can provide win-win outcomes toward efficient mobility (high demand coverage, low operating costs, high level of service), equitable mobility (broad geographic reach) and sustainable mobility (limited environmental footprint).

Orateur: Bernardo Martin-Iradi (ETH Zurich)

Chance-constrained programming: Contributed talks

Président de session: Csaba Fabian (John von Neumann University)

77 Statistical Performance of Subgradient Step-Size Update Rules in Lagrangian Relaxations of Chance-Constrained Optimization Models

Lagrangian relaxation schemes, coupled with a subgradient procedure, are frequently employed to solve chance-constrained optimization models. Subgradient procedures typically rely on step-size update rules. Although there is extensive research on the properties of these step-size update rules, there is little consensus on which rules are most suitable practically; especially, when the underlying model is a computationally challenging instance of a chance-constrained program. To close this gap, we seek to determine whether a single step-size rule can be statistically guaranteed to perform better than others. We couple the Lagrangian procedure with three strategies to identify lower bounds for two-stage chance-constrained programs. We consider two instances of such models that differ in the presence of binary variables in the second-stage. With a series of computational experiments, we demonstrate—in marked contrast to existing theoretical results—that no significant statistical differences in terms of optimality gaps is detected between six well-known step-size update rules. Despite this, our results demonstrate that a Lagrangian procedure provides computational benefit over a naive solution method—regardless of the underlying step-size update rule.

This work is published here: https://doi.org/10.1007/978-3-031-47859-8_26.

Orateur: Dr Bismark Singh (University of Southampton)

78 Random descent steps in a probability maximization scheme

Gradient computation of multivariate distribution functions calls for a considerable effort. Hence coordinate descent and derivative-free approaches are attractive. This talk deals with constrained convex problems. We perform random descent steps in an approximation scheme that is an inexact cutting-plane method from a dual viewpoint. We prove that the scheme converges and present a computational study comparing different descent methods applied in the approximation scheme.

Orateur: Csaba Fabian (John von Neumann University)

79 Convexity of elliptically distributed chance constraints with copula structures dependent on decision variables

Chance constraints describe a set of given random inequalities depending on the decision vector satisfied with a large enough probability. They are widely used in decision making under uncertain data in many engineering problems. This talk aims to derive the convexity of chance constraints with elliptically distributed dependent rows via a Gumbel-Hougaard copula. The eventual convexity of chance constraints is separated as the concavity and convexity of two auxiliary functions: the first one is a probability function, and a copula's generator defines the second one. For the probability function, comparing to the $r$-concavity results with $r = -2$ in [1] and $r < -1 $ in [2], we obtain the thresholds of the $r$-concavity for any real number $r$. Then, we improve probability thresholds of the eventual convexity, which are all less than the thresholds in [1, 2, 3]. With respect to the function defined by a copula's generator, we extend the assumptions about the copula and the domain $\Omega$ without the origin in [3] and estimate the singularity of Gumbel-Hougaard copulas around the origin, where the singularity can lead to the copula's unboundedness. Finally, we prove the eventual convexity with elliptical distributions and a Gumbel-Hougaard copula despite the copula's singularity near the origin. To illustrate our results, we provide an example with the eventual convexity of a feasible set containing the origin.

References
[1] R Henrion and C Strugarek. Convexity of chance constraints with independent random variables. Computational Optimization and Applications, 41(2):263–276, 2008.
[2] J Cheng, M Houda, and A Lisser. Chance constrained 0–1 quadratic programs using copulas. Optimization Letters, 9:1283–1295, 2015.
[3] H N Nguyen, A Lisser, and J Liu. Convexity of linear joint chance constrained optimization with elliptically distributed dependent rows. Results in Control and Optimization, 12:100285, 2023.

Orateur: Heng Zhang (Paris-Saclay University, CNRS, CentraleSupelec, Laboratory of signals and systems)

80 Chance-constrained zero-sum stochastic games

We consider a two-person zero-sum discounted stochastic game with random rewards and known transition probabilities. The players have opposite objectives and are interested in optimizing the expected discounted reward which they can obtain with a given confidence level when both the players play the worst possible move against each other.
We model such a game problem by defining the chance-constrained optimization problem of each player, and call this new formulation a chance-constrained stochastic game (CCSG). When the reward vector follows a multivariate elliptically symmetric distribution, the CCSG is equivalent to a minimax formulation. We consider CCSG with risk seeking and risk averse players separately.

We show that the risk-seeking problem is equivalent to a constrained optimization of a parameterized zero-sum stochastic game and the optimal payoff of player 1 and optimal cost of player 2 can be computed using algorithms based on a fixed point iteration. Later we can use the fixed point solutions to compute players' optimal strategies by solving linear programming problems.

We reformulate the risk averse problem as a discrete minimax problem. We propose an algorithm based on a linearization method and discuss its
convergence properties. Alternatively, we reformulate the risk averse problem as a second-order cone programming problem with bilinear constraints.
We illustrate the theoretical results with numerical experiments.

Orateur: Lucas Osmani (Laboratoire des signaux et systèmes)

Presentation_ICSP_2025.pdf

ML: Functional Models In Stochastic Optimization

Président de session: Andrzej Ruszczynski (Rutgers University)

81 Optimal mass transportation relaxations of stochastic dominance relations in optimization

Optimization problem with stochastic dominance constraints provide a possibility to shape risk by selecting a benchmark random outcome with a desired distribution. A difficulty arises when no feasible decision results in a distribution that dominates the benchmark. In this talk, we address the problem of choosing a tight relaxation of the stochastic dominance constraint by selecting a feasible distribution, which is closest to the benchmark in terms of a mass transportation distance. For the second-order stochastic dominance, we present new formulae for the Monge-Kantorovich distance of first order of a given distribution to the set of distributions dominating the benchmark. Under an additional assumption, we also construct the associated projection. The results allow us to construct numerical methods for solving the optimization problem with automatic relaxation should the benchmark cause infeasibility. We present also numerical results illustrating the proposed approach.

Orateur: Darinka Dentcheva (Stevens Institute of Technology)

82 A Functional Model Method for Nonconvex Nonsmooth Conditional Stochastic Optimization

We consider stochastic optimization problems involving an expected value of a nonlinear function of a base random vector and a conditional expectation of another function depending on the base random vector, a dependent random vector, and the decision variables. We call such problems conditional stochastic optimization problems. They arise in many applications, such as uplift modeling, reinforcement learning, and contextual optimization.
We propose a specialized single time-scale stochastic method for nonconvex constrained conditional stochastic optimization problems with a Lipschitz smooth outer function and a generalized differentiable inner function. In the method, we approximate the inner conditional expectation with a rich parametric model whose mean squared error satisfies a stochastic version of a Lojasiewicz condition. The model is used by an inner learning algorithm. The main feature of our approach is that unbiased stochastic estimates of the directions used by the method can be generated with one observation from the joint distribution per iteration, which makes it applicable to real-time learning. The directions, however, are not gradients or subgradients of any overall objective function. We prove the convergence of the method with probability one, using the method of differential inclusions and a specially designed Lyapunov function, involving a stochastic generalization of the Bregman distance. Finally, a numerical illustration demonstrates the viability of our approach.

Orateur: Andrzej Ruszczynski (Rutgers University)

83 Measures of stochastic non-dominance

Stochastic dominance rules are well-characterized and widely used. This work aims to describe and better understand the situations when they do not hold by developing measures of stochastic non-dominance. They quantify the error caused by assuming that one random variable dominates another one when it does not. To calculate them, we search for a hypothetical random variable that satisfies the stochastic dominance relationship and is as close to the original one as possible. The Wasserstein distance between the optimal hypothetical random variable and the original one is considered as the measure of stochastic non-dominance. Depending on the conditions imposed on the probability distribution of the hypothetical random variable, we distinguish between general and specific measures of stochastic non-dominance. We derive their exact values for random variables with uniform, normal, and exponential distributions. We present relations to almost first-order stochastic dominance and to tractable almost stochastic dominance. Using monthly returns of twelve assets captured by the German stock index DAX, we solve portfolio optimization problems with the first-order and second-order stochastic dominance constraints. The measures of stochastic non-dominance allow us to compare the optimal portfolios with respect to different orders of stochastic dominance from a new angle.

Orateur: Milos Kopa

Stochastic integer programming: Large-Scale and HPC-Based Computation

Président de session: Jean-Paul Watson (Lawrence Livermore National Laboratory)

84 What's new in MPI-SPPY

MIP-SPPY is software for stochastic programming that can run on a laptop, but uses MPI (message passing interface) to perform well on distributed memory computers. In this talk I will talk about high level changes to the user interface and low level changes to the way we manage interaction between algorithms running asynchronously in parallel.

Orateur: David Woodruff (UC Davis)

85 Large-Scale Experimentation and Analysis of HPC-Based Scenario Decomposition via Progressive Hedging with mpi-sppy

Parallel implementations of scenario-based decomposition strategies are now scalable to thousands and millions of scenarios, thanks to advances in modeling systems (e.g.., Pyomo) and supporting meta-solvers (e.g., mpi-sppy). We describe challenges and their solution considering a large-scale power grid capacity expansion model, where scenarios represent individual days of weather. We discuss in detail various algorithmic tuning and approaches to rapidly finding high-quality solutions to these stochastic programs, utilizing the mpi-sppy meta-solver library.

Orateur: Jean-Paul Watson (Lawrence Livermore National Laboratory)

86 High-Order Binary Optimization Formulations of Influence Maximization Problem for Efficient Quantum Computing

The Influence Maximization Problem (IMP), which seeks to identify influential nodes in a network to maximize expected information spread, is inherently stochastic and NP-hard—making it a natural candidate for quantum optimization methods. Classical approaches typically formulate IMP as a deterministic optimization problem (e.g., via sample average approximation), then encode it as a Quadratic Unconstrained Binary Optimization (QUBO) problem. However, enforcing coverage-type constraints in QUBO formulations often requires auxiliary slack variables, resulting in substantial overhead and limiting scalability. In this work, we introduce a novel High-Order Binary Optimization (HOBO) formulation for IMP that directly captures the constraint logic without slack variables. Specifically, we reformulate common constraints of the form $y \le \sum x_j$ using compact product-based expressions, applicable when the sum includes a small number of terms. This leads to a parametric HOBO model that enables a tunable trade-off between reducing variable count and managing the complexity of higher-order interactions. We establish rigorous theoretical bounds for penalty parameters and validate the approach through extensive experiments on stochastic network instances drawn from Erdös-Renyi and Scale-Free graphs. Compared to standard QUBO formulations, our HOBO model yields faster solution times, lower variance in performance across samples, and high-quality solutions. These results highlight HOBO formulations as an efficient and scalable alternative for solving smaller IMP on current quantum hardware.

Orateur: Prof. Joachim Ehrenthal (University of Applied Sciences and Arts Northwestern Switzerland FHNW)

Mini-symposium: Student Prize

Président de session: Jim Luedtke (University of Wisconsin-Madison)

87 Solving Two-Stage Programs with Endogenous Uncertainty via Random Variable Transformation

Real-world decision-making problems often involve decision-dependent uncertainty, where the probability distribution of the random vector depends on the model's decisions. Few studies focus on two-stage stochastic programs with this type of endogenous uncertainty, and those that do lack general methodologies. We propose a general method for solving a class of these programs based on random variable transformation, a technique widely employed in probability and statistics. The random variable transformation converts a stochastic program with endogenous uncertainty (original program) into an equivalent stochastic program with decision-independent uncertainty (transformed program), for which solution procedures are well-studied. Additionally, endogenous uncertainty usually leads to nonlinear nonconvex programs, which are theoretically intractable. Nonetheless, we show that, for some classical endogenous distributions, the proposed method yields mixed-integer linear or convex programs with exogenous uncertainty. We validate this method by applying it to a network design and facility-protection problem, considering distinct decision-dependent distributions for the random variables. While the original formulation of this problem is nonlinear nonconvex for most endogenous distributions, the proposed method transforms it into mixed-integer linear programs with exogenous uncertainty. We solve these transformed programs with the sample average approximation method. We highlight the superior performance of our approach compared to solving the original program in the case a mixed-integer linear formulation of this program exists.

Orateur: Maria Carolina Bazotte Corgozinho (CIRRELT, Polytechnique Montreal)

88 Convex Chance-Constrained Programs with Wasserstein Ambiguity

AChance constraints yield nonconvex feasible regions in general. In particular, when the uncertain parameters are modeled by a Wasserstein ball, existing studies showed that the distributionally robust (pessimistic) chance constraint admits a mixed-integer conic representation. This talk identifies sufficient conditions that lead to convex feasible regions of chance constraints with Wasserstein ambiguity. First, when uncertainty arises from the right-hand side of a pessimistic joint chance constraint, we show that the ensuing feasible region is convex if the Wasserstein ball is centered around a log-concave distribution (or, more generally, an α-concave distribution with 𝛼≥−1 ). In addition, we propose a block coordinate ascent algorithm and prove its convergence to global optimum, as well as the rate of convergence. Second, when uncertainty arises from the left-hand side of a pessimistic two-sided chance constraint, we show the convexity if the Wasserstein ball is centered around an elliptical and star unimodal distribution. In addition, we propose a family of second-order conic inner approximations, and we bound their approximation error and prove their asymptotic exactness. Furthermore, we extend the convexity results to optimistic chance constraints.

Orateur: Haoming Shen (University of Arkansas, USA)

89 Towards Optimal Offline Reinforcement Learning

We study offline reinforcement learning problems with a long-run average reward objective. The state-action pairs generated by any fixed behavioral policy thus follow a Markov chain, and the empirical state-action-next-state distribution satisfies a large deviations principle. We use the rate function of this large deviations principle to construct an uncertainty set for the unknown true state-action-next-state distribution. We also construct a distribution shift transformation that maps any distribution in this uncertainty set to a state-action-next-state distribution of the Markov chain generated by a fixed evaluation policy, which may differ from the unknown behavioral policy. We prove that the worst-case average reward of the evaluation policy with respect to all distributions in the shifted uncertainty set provides, in a rigorous statistical sense, the least conservative estimator for the average reward under the unknown true distribution. This guarantee is available even if one has only access to one single trajectory of serially correlated state-action pairs. The emerging robust optimization problem can be viewed as a robust Markov decision process with a non-rectangular uncertainty set. We adapt an efficient policy gradient algorithm to solve this problem. Numerical experiments show that our methods compare favorably against state-of-the-art methods.

Orateur: Mengmeng Li (EPFL)

90 Optimizer's Information Criterion: Dissecting and Correcting Bias in Data-Driven Optimization

In data-driven optimization, the sample performance of the obtained decision typically incurs an optimistic bias against the true performance, a phenomenon commonly known as the Optimizer's Curse and intimately related to overfitting in machine learning. We develop a general approach that we call Optimizer's Information Criterion (OIC) to correct this bias. OIC generalizes the celebrated Akaike Information Criterion from the evaluation of model adequacy, used primarily for model selection, to objective performance in data-driven optimization which is used for decision selection. Our approach analytically approximates and cancels out the bias that comprises the interplay between model fitting and downstream optimization. As such, it saves the computation need to repeatedly solve optimization problems in cross-validation, while operates more generally than other bias approximating scheme. We apply OIC to a range of data-driven optimization formulations comprising empirical and parametric models, their regularized counterparts, and furthermore contextual optimization. Finally, we provide numerical validation on the superior performance of our approach under synthetic and real-world datasets.

Orateur: Tianyu Wang

91 Multistage Distributionally Robust Mixed-Integer Programming with Decision-Dependent Moment-Based Ambiguity Sets

We study multistage distributionally robust mixed-integer programs under endogenous uncertainty, where the probability distribution of stage-wise uncertainty depends on the decisions made in previous stages. We first consider two ambiguity sets defined by decision-dependent bounds on the first and second moments of uncertain parameters and by mean and covariance matrix that exactly match decision-dependent empirical ones, respectively. For both sets, we show that the subproblem in each stage can be recast as a mixed-integer linear program (MILP). Moreover, we extend the general moment-based ambiguity set in Delage and Ye (2010) to the multistage decision-dependent setting, and derive mixed-integer semidefinite programming (MISDP) reformulations of stage-wise subproblems. We develop methods for attaining lower and upper bounds of the optimal objective value of the multistage MISDPs, and approximate them using a series of MILPs. We deploy the Stochastic Dual Dynamic integer Programming (SDDiP) method for solving the problem under the three ambiguity sets with risk-neutral or risk-averse objective functions, and conduct numerical studies on multistage facility-location instances having diverse sizes under different parameter and uncertainty settings. Our results show that the SDDiP quickly finds optimal solutions for moderate-sized instances under the first two ambiguity sets, and also finds good approximate bounds for the multistage MISDPs derived under the third ambiguity set. We also demonstrate the efficacy of incorporating decision-dependent distributional ambiguity in multistage decision-making processes.

Orateur: Xian Yu (The Ohio State University)

Mini-symposium: Taming the Curse of Dimension in Multistage Stochastic Programming

Président de session: Yifan Hu (EPFL)

92 Contextual Stochastic Bilevel Optimization

We introduce contextual stochastic bilevel optimization (CSBO) - a stochastic bilevel optimization framework with the lower-level problem minimizing an expectation conditioned on contextual information and on the upper-level decision variable. We also assume that there may be multiple (or even infinitely many) followers at the lower level. CSBO encapsulates important applications such as meta-learning, personalized federated learning, end-to-end learning, and Wasserstein distributionally robust optimization with side information as special cases. Due to the contextual information at the lower level, existing single-loop methods for classical stochastic bilevel optimization are not applicable. We thus propose an efficient double-loop gradient method based on the Multilevel Monte-Carlo (MLMC) technique. When specialized to stochastic nonconvex optimization, the sample complexity of our method matches existing lower bounds. Our results also have important ramifications for three-stage stochastic optimization and challenge the long-standing belief that three-stage stochastic optimization is harder than classical two-stage stochastic optimization.

Orateur: Daniel Kuhn (EPFL)

93 Taming the Curse of Dimension/Horizon in Multistage Stochastic Programming

Algorithms for solving Multistage Stochastic Programming (MSP) are long known to suffer from the curse of dimension and horizon. Stochastic Dual Dynamic Programming (SDDP) for stage-wise independence MSP problem admits a complexity of scales exponentially with respect to the decision dimension $d$ in terms of accuracy $\epsilon$, i.e., $O(\epsilon^{-d})$. On the other hand, Stochastic Approximation (SA) and Sample Average Approximation (SAA) type of methods admit a complexity that scales exponentially with respect to the horizon $T$, i.e., $O(\epsilon^{-T})$ for general MSP. In this talk, we discuss a novel approximation-based algorithm that achieves $O(poly(1/\epsilon))$ dependence in a class of MSP problems.

Orateur: Yifan Hu (EPFL)

94 Multilevel Conditional Compositional Estimation and Optimization

We introduce Multilevel Conditional Compositional Optimization (MCCO) as a new framework for decision-making under uncertainty that combines aspects of multistage stochastic programming and conditional stochastic optimization. MCCO minimizes a nest of conditional expectations and nonlinear cost functions. It finds wide applications in optimal stopping, credit valuation adjustments, distributionally robust contextual bandits, and nested risk minimization. The naive nested sampling approach for MCCO suffers from the curse of dimensionality familiar from scenario tree-based multistage stochastic programming, that is, its sample complexity grows exponentially with the number of nests. We develop new multilevel Monte Carlo techniques for MCCO whose sample complexity grows only polynomially with the desired accuracy.

Orateur: Buse Şen (EPFL)

12:45 Lunch

95 CMS editors meeting

Stochastic Programming: Contributed talks

Président de session: Anton Kleywegt (Georgia Institute of Technology)

96 Nonstationary Distribution Estimation Via Wasserstein Probability Flows

We consider a situation in which observations are made from an underlying distribution that changes over time. We use a non-parametric model for the changes in distribution and suppose that the change is most likely to involve a small Wasserstein distance between two successive distributions. This leads naturally to a formulation in which we estimate the underlying set of distributions through maximising the log likelihood of the observations with a penalty applied to the total of the Wasserstein distances between successive probability distributions. We call this the Wasserstein Probability Flow (WPF) problem and we show how it reduces to a simple network flow problem. This can be easily solved, and we derive some properties of optimal solutions. We also show with numerical experiments how the WPF approach can be effective in practice.

Orateur: Edward Anderson (Imperial College London)

97 Design Optimization and Derivative-Free Optimization

In derivative-free optimization one has access to a zeroth-order oracle, that is, a black box that takes a feasible point as input and provides the objective value at the point, possibly random, as output, but it provides no derivatives. This setting is encountered in many science and engineering applications, and often each call to the black box is expensive. An important approach to derivative-free optimization is to use objective values at selected design points to approximate derivatives. Careful selection of the points, and reuse of objective values at previously selected points, is important for algorithm performance, especially when black box calls are expensive. We propose an optimization-based algorithm to select points for a local first-order regression model and a local second-order regression model, with possible reuse of previously selected points. The performance of the designs are tested in various derivative-free optimization algorithms.

Orateur: Anton Kleywegt (Georgia Institute of Technology)

98 Scenario Tree Design under Wasserstein and Fused Gromov-Wasserstein Distances

A central challenge in multi-stage stochastic programs (MSP) lies in constructing scenario trees that approximate the underlying stochastic process with sufficient accuracy while maintaining computational tractability. In this work, we consider the case where the true stochastic process is discretely distributed, and the topology of the approximating scenario tree is fixed.
We propose two novel scenario tree approximation methods grounded in optimal transport theory. The first approach minimizes the stagewise Wasserstein distance between the empirical distributions of the true process and those induced by the scenario tree, ensuring stage-by-stage closeness. The second approach leverages the Fused Gromov-Wasserstein (FGW) distance, which integrates both the feature-level differences (captured by the Wasserstein distance) and structural discrepancies (captured by the Gromov-Wasserstein distance) between distributions. This is particularly suitable for scenario trees, which are structured objects combining probabilistic and topological information.
Both approaches formulate the scenario tree generation as a continuous, nonconvex optimization problem. To solve this, we employ a block coordinate descent method that alternates between optimizing over the discrete distribution assignments and the associated cost structure. This enables efficient computation while preserving fidelity to the underlying stochastic process.
Our methods offer a principled way to balance the trade-off between approximation accuracy and computational feasibility.

Orateur: Andrew Schaefer (Rice University)

99 Constant Depth Decision Rules for multistage optimization under uncertainty

In this paper, we introduce a new class of decision rules, referred to as Constant Depth Decision Rules (CDDRs), for multistage optimization under linear constraints with uncertainty-affected right-hand sides. We consider two uncertainty classes: discrete uncertainties which can take at each stage at most a fixed number d of different values, and polytopic uncertainties which, at each stage, are elements of a convex hull of at most d points. Given the depth mu of the decision rule, the decision at stage t is expressed as the sum of t functions of mu consecutive values of the underlying uncertain parameters. These functions are arbitrary in the case of discrete uncertainties and are poly-affine in the case of polytopic uncertainties. For these uncertainty classes, we show that when the uncertain right-hand sides of the constraints of the multistage problem are of the same additive structure as the decision rules, these constraints can be reformulated as a system of linear inequality constraints where the numbers of variables and constraints is O(1)(n+m)d^mu N^2 with n the maximal dimension of control variables, m the maximal number of inequality constraints at each stage, and N the number of stages. As an illustration, we discuss an application of the proposed approach to a Multistage Stochastic Program arising in the problem of hydro-thermal production planning with interstage dependent inflows. For problems with a small number of stages, we present the results of a numerical study in which optimal CDDRs show similar performance, in terms of optimization objective, to that of Stochastic Dual Dynamic Programming (SDDP) policies, often at much smaller computational cost.

Orateur: Vincent Guigues (FGV)

(Distributionally) Robust Optimization: Advancing Robust/Data-Driven Optimization Strategies for Resilience and Social Impact

Président de session: Cagil Kocyigit (University of Luxembourg)

100 Process Flexibility: A Distribution-Free Approach to Long Chain Resilience

Process flexibility has been a well-established supply chain strategy in both theory and practice that enhances responsiveness to demand uncertainty. In this study, we expand the scope of this strategy to supply disruption mitigation by analyzing a long chain system. Specifically, we investigate the effectiveness of long chains in the face of random supply disruptions and demand uncertainty. Our study derives a closed-form, tight bound on the ratio of expected sales under supply disruption for a long chain relative to that of a fully flexible system, thereby providing a service level guarantee. Our analysis provides a concrete analytical result demonstrating that the fraction of benefits a long chain can achieve relative to full flexibility increases in the disruption probability when designed capacity equals expected demand. Also, the long chain demonstrates superior resilience by withstanding a non-negligible fraction of the supply disruption due to its relatively sparse structure compared to a fully flexible system.

To generalize the analysis, we introduce a moment decomposition approach that readily adapts to general piecewise polynomial performance metrics and allows the capacity to differ from the expected demand. This approach encompasses the traditional type-II service metric (expected sales) as well as the type-I metric (probability of meeting full demand), with the latter representing a novel contribution to the existing literature. Our approach can also incorporate higher-moment information (such as skewness and kurtosis) on the random demand while maintaining tractability through a semidefinite program (SDP). We apply this approach to study the capacity configuration problem. Our study reveals that, in the absence of supply disruption, attaining a specific service level requires a capacity level close to that of a fully flexible system, even when the demand distribution is only partially characterized. In contrast, a notable increase in capacity is required under supply disruption. Yet, the long chain significantly outperforms a dedicated system in capacity requirement. Our findings underscore the remarkable resilience demonstrated by long chains and the importance of adapting capacity configuration decisions to supply disruption.

Orateur: LI CHEN

101 Distribution-Free Auctions: Balancing Regret, Equity, and Opacity

We study a mechanism design problem where a seller aims to allocate a good to multiple bidders, each with a private value. The seller supports or favors a specific group, referred to as the minority group. Specifically, the seller requires that allocations to the minority group are at least a predetermined fraction (equity level) of those made to the rest of the bidders. Such constraints arise in various settings, including government procurement and corporate supply chain policies that prioritize small businesses, environmentally responsible suppliers, or enterprises owned by historically disadvantaged individuals. We analyze two variants of this problem: stochastic mechanism design, which assumes bidders’ values follow a known distribution and seeks to maximize expected revenue, and regret-based mechanism design, which makes no distributional assumptions and aims to minimize the worst-case regret. We characterize a closed-form optimal stochastic mechanism and propose a closed-form regret-based mechanism, and establish that the ex-post regret under the latter is at most a constant multiple (dependent on the equity level) of the optimal worst-case regret. We further quantify that this approximation constant is at most 1.31 across different equity levels. Both mechanisms can be interpreted as set-asides, a common policy tool that reserves a fraction of goods for minority groups. Furthermore, numerical results demonstrate that the stochastic mechanism performs well when the bidders’ value distribution is accurately estimated, while the regret-based mechanism exhibits greater robustness under estimation errors.

Orateur: Prof. Napat Rujeerapaiboon (National University of Singapore)

102 From Data to Donations: Optimal Fundraising Campaigns for Non-Profit Organizations

Non-profit organizations play a vital role in addressing global challenges, yet their financial sustainability often hinges on the effectiveness of their fundraising campaigns. We collaborate with a major international non-profit organization to develop and test data-driven approaches to increase the efficiency of their fundraising efforts. Our partner organization conducts multiple annually recurring campaigns, which are thematically linked. The short lifespan of individual donors necessitates efficient learning of both the connections between campaigns and response patterns across donors. To this end, we propose two learning algorithms that integrate principles from multi-armed bandits and clustering. We provide theoretical guarantees for these algorithms and validate their performance on real-world data from our partner organization. The results highlight the potential to significantly enhance the organization's fundraising effectiveness.

Orateur: Zhengchao Wang (Imperial College London)

103 Learning Robust Risk Scores from Observational Data under Unobserved Confounders

We consider the problem of learning, from observational data, a logistic regression model to predict the risk of an adverse outcome under no treatment. These problems arise routinely in public health and the social sciences, e.g., to help prioritize individuals for scarce resources or services. The vast majority of the literature on the topic assumes unconfoundedness, i.e., no unobserved confounders affect both treatment assignments and outcomes. However, this assumption often fails to hold in practice. In this research, we propose a logistic regression-based risk prediction model that is robust to potential unobserved confounders. Our approach constructs uncertainty sets for inverse propensity weights, inspired by sensitivity analysis in causal inference and Wasserstein distributionally robust optimization. We demonstrate the effectiveness of our approach on a set of synthetic data and semi-synthetic data, showing that our robust approach achieves better performance compared to the baseline non-robust approaches. We also conduct a case study on scarce housing resource allocation to people experiencing homelessness, based on the real data from LA County Homeless Management Information System.

Orateur: Cagil Kocyigit (University of Luxembourg)

Application in energy, finance or logistics: Contributed talks

Président de session: Giorgio Consigli (Khalifa University of Science and Technology)

104 Portfolio selection using stochastic non-dominance constraints

We extend portfolio selection models with classical stochastic dominance constraints by allowing a controlled violation of these constraints. This relaxation permits the returns of feasible portfolios to differ from those that stochastically dominate the benchmark within a tolerance measured by the Wasserstein distance. We formulate an optimization problem that incorporates the stochastic non-dominance constraints, assuming discrete distributions of returns. Additionally, we examine the relationship between this approach and portfolio models based on almost stochastic dominance. To assess the proposed method, we apply the second-order stochastic non-dominance constraints to the portfolio selection problem using a dataset of daily returns from 49 U.S. industry representative portfolios. A moving-window analysis over 96 years demonstrates that allowing small levels of stochastic non-dominance, particularly when measured by the Wasserstein distance of order two, can increase out-of-sample returns while maintaining a similar level of risk compared to the classical second-order stochastic dominance approach.

Orateur: Jana Junova (Charles University)

105 Bi-level Stochastic Portfolio Optimization Problem based on SSD Portfolio Efficiency

It is a common practice in portfolio optimization to focus on the minimization of losses and risk. However, more advanced models incorporating the second-order stochastic dominance (SSD) constraints have gained increasing attention in last two decades. These constraints identify the portfolios that dominate the benchmark portfolio with respect to SSD. Contrary to that, this paper is focused on the feasibility conditions that ensure portfolio efficiency with respect to SSD — in other words, only portfolios which are not dominated by any other portfolio are considered as feasible ones in the model. Moreover, if we seek to optimize an additional criterion with respect to the SSD feasibility set — such as maximizing the return or minimizing the risk — the resulting model becomes a stochastic bi-level optimization problem. The lower level problem guarantees the SSD efficiency, while the upper level problem optimizes the selected criterion. We formulate, analyze and solve such stochastic bi-level optimization problem under various upper level objectives, including the minimization of transaction costs or the maximization of out-of-sample mean returns. The advantages of these models are demonstrated through empirical results based on the out-of-sample performance and moving window analysis using real-life market data.

Orateur: Monika Kaľatová (Charles University, Department of Probability and Mathematical Statistics)

106 Optimal multiperiod portfolio risk-distribution based on reinforcement learning

In an early paper we have studied the correspondence between second order interval stochastic dominance (ISD-2) and interval conditional value-at-risk (ICVaR), a tail risk measure carrying specific properties and generalizing the popular conditional value-at-risk.
Relying on the ICVaR, in this paper, we present a reinforcement learning approach to solve a trade-off problem based on one side on a risk parity paradigm and on the other on an ICVaR function enforcing second order dominance with respect to a benchmark strategy. The bi-criteria objective helps clarifying the risk-budgeting implications induced by a progressive switch from risk parity towards SD against the benchmark for portfolio
construction in a dynamic model. Throughout the model formulation we focus jointly on the evolution of the risk- and the asset-composition of optimal asset portfolios. We consider a 1-year investment problem with monthly rebalancing and exclude short portfolio positions. The asset universe, or decision space of the problem, is based on exchange traded funds (ETF) and market benchmarks spanning different risk classes. The adoption of a reinforcement learning (RL) approach, under the given assumptions, has two main motivations: the relevant curse of dimensionality associated with a multistage stochastic programming (MSP) or stochastic dynamic programming (SDP) formulations as well as the
recent advances in machine learning thanks to the development of convex reinforcement learning (CRL) techniques, which are here thoroughly evaluated. An extended in- and out-of-sample validation is performed on market data from 2018 to 2024 with a discussion on the computational properties of the problem.

Orateur: Giorgio Consigli (Khalifa University of Science and Technology)

Game theory and equilibrium: Contributed talks

Président de session: Bernardo Pagnoncelli (SKEMA Business School)

107 New Approaches to Multistage Equilibrium Problems in Economics

In this study, we examine multistage problems involving multiple agents, commonly known as stochastic dynamic games. Solving such problems is particularly challenging in real-world scenarios with a large number of interacting agents. We present a general formulation and focus on an incomplete market, heterogeneous agent model with aggregate uncertainty—the Krusell-Smith model. Our numerical exploration begins by reviewing traditional strategies for deriving equilibrium solutions, starting with the moment approach originally proposed by Krusell and Smith (1998). We then introduce a novel method that departs from the assumption of a predefined functional form for agents' capital dynamics. Instead, our approach iteratively constructs a Markov Chain based on the states visited, offering greater flexibility in capturing equilibrium dynamics. Finally, we discuss how these techniques can be extended to heterogeneous agent New Keynesian (HANK) models. These models have become an essential framework for central banks, enabling them to analyze the distributional effects of monetary policy and better understand the link between macroeconomic fluctuations and inequality.

Orateur: Bernardo Pagnoncelli (SKEMA Business School)

108 Learning in Games with progressive hiding

When learning to play an imperfect information game, it is often easier to first start with the basic mechanics of the game rules.
For example, one can play several example rounds with private cards revealed to all players to better understand the basic actions and their effects. Building on this intuition, this paper introduces {\it progressive hiding}, an algorithm that learns to play imperfect information games by first learning the basic mechanics and then progressively adding information constraints over time.
Progressive hiding is inspired by methods from stochastic multistage optimization such as scenario decomposition and progressive hedging.
We prove that it enables the adaptation of counterfactual regret minimization to games where perfect recall is not satisfied. Numerical experiments illustrate that progressive hiding can achieve optimal payoff in a benchmark of emergent communication trading game.

Orateur: Benjamin Heymann

109 A Differentiable Path-Following Method to Compute Nash Equilibria in Behavioral Strategies for Robust Extensive-Form Games

An extension of robust optimization to extensive-form games with payoff uncertainty yields robust extensive-form games. To compute Nash equilibria in behavioral strategies for robust extensive-form games with perfect recall, we acquire from a characterization a polynomial system as a necessary and sufficient condition of Nash equilibrium in robust extensive-form games. As a result of this condition, this paper develops a differentiable path-following method to compute Nash equilibria. Incorporating a logarithmic-barrier term into each player's payoff function with an extra variable, we constitute a logarithmic-barrier robust extensive-form game in which each player solves at each information set a convex optimization problem. Applying the optimality conditions to the barrier game and the equilibrium condition yields a polynomial equilibrium system for the barrier game. As a result of this system, we establish the existence of a smooth path that starts from an arbitrary totally mixed behavioral strategy profile and ends at a Nash equilibrium as the extra variable vanishes. For numerical comparisons, we formulate, as an alternative scheme, a convex-quadratic-penalty robust extensive-form game and secure a globally convergent convex-quadratic-penalty differentiable path-following method for Nash equilibria in robust extensive-form games. Numerical comparisons show that the logarithmic-barrier path-following method significantly outperforms the convex-quadratic-penalty path-following method.

Orateur: Yiyin Cao (Xi'an Jiaotong University)

110 Continuous and Monotone Bayesian Nash Equilibrium with Incomplete Information about Player's Risk Preferences

In this paper, we consider a non-collaborative game where each player faces two types of uncertainties: aleatoric uncertainty arising from inherent randomness of underlying data in its own decision-making problem and epistemic uncertainty arising from lack of knowledge and statistical information on the rivals' risk preferences. By assuming that players are risk-averse against aleatoric uncertainty and risk-neutral on the epistemic uncertainty, we propose a Bayesian risk minimization model to describe players' interactions. We investigate existence and uniqueness of a continuous monotone equilibrium arising from the game, termed CMBNRE, where ``R'' is used to emphasize the game is concerned with risk minimization as opposed to utility maximization in the existing BNE models. We derive sufficient and/or necessary conditions for ensuring existence of CMBNRE from two perspectives: monotonicity of a continuous BNRE and continuity of a monotone BNRE. Continuous BNE emphasizes continuity of each player's response function with respect to variation of the type parameter whereas monotone BNE focuses on monotonicity of the player's response function and/or rival's response functions. The former is derived by virtue of Schauder's fixed point theorem and the latter is established by other fixed point theorems based on single-crossing and quasi-supermodularity, the proposed CMBNRE model synthesizes the two modeling frameworks. We discuss numerical methods for computing an approximate CMBNRE from stochastic optimization perspective and apply the proposed model and computational schemes to a reinsurance competition problem. The test results provide some insights about how indemnity parameter may affect reinsurer's behaviour, market share and profitability.

Orateur: M. Ziheng Su (The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management)

ML: Contributed talks

Président de session: Sebastian Maier

111 Guaranteed bounds for optimal stopping problems using kernel-based non-asymptotic uniform confidence bands

In this paper, we introduce an approach for obtaining probabilistically guaranteed upper and lower bounds on the true optimal value of stopping problems. Bounds of existing simulation-and-regression approaches, such as those based on least squares Monte Carlo and information relaxation, are stochastic in nature and therefore do not come with a finite sample guarantee. Our data-driven approach is fundamentally different as it allows replacing the sampling error with a pre-specified confidence level. The key to this approach is to use high- and low-biased estimates that are guaranteed to over- and underestimate, respectively, the conditional expected continuation value that appears in the stopping problem's dynamic programming formulation with a pre-specified confidence level. By incorporating these guaranteed over- and underestimates into a backward recursive procedure, we obtain probabilistically guaranteed bounds on the problem’s true optimal value. As a byproduct we present novel kernel-based non-asymptotic uniform confidence bands for regression functions from a reproducing kernel Hilbert space. We derive closed-form formulas for the cases where the data-generating distribution is either known or unknown, which makes our data-driven approach readily applicable in a range of practical situations including simulation. We illustrate the applicability of the proposed bounding procedure by valuing a Bermudan put option.

Orateur: Sebastian Maier (University College London)

112 Data-Driven Modeling of Endogenous Uncertainty in Optimization

Decision-makers often face complex problems under uncertainty. Statistical and Machine Learning (ML) tools can support these decisions by reducing the lack of knowledge. However, in many real-world scenarios, the uncertainty itself is induced by the decisions taken. In such cases, standard ML models that provide a priori insights of the problem environment become ineffective. In the context of decision-dependent uncertainty, a promising approach is Constraint Learning (CL). According to this procedure, a pretrained ML model is embedded into the optimization model to capture relationships between uncertain parameters and decision variables that must be set in advance. However, the dependency between decision and response variables is often not known with certainty due to epistemic errors in the prediction model. To address this limitation within a robust optimization framework, we propose an extension of CL that constructs decision-dependent uncertainty sets using a Quantile Surface Neural Network (QSNN). The QSNN learns multi-dimensional conditional quantile functions from data, allowing the characterization of uncertainty that varies across the decision space. Since embedding neural networks within optimization problems introduces additional complexity, we propose an initial solution approach to handle this integration effectively. To demonstrate the practical relevance of our methodology, we apply it to an energy hub management problem. In this case study, the energy consumption of a group of users is partially sensitive to the day-ahead tariff set by the hub. Preliminary results highlight the potential of the proposed approach in managing demand-side uncertainty and improving operational efficiency.

Orateur: Dr Luigi Gallo (Department of Mechanical, Energy, and Management Engineering, University of Calabria, Italy)

113 Federated Learning with Sample Selection: A Robust Optimization Approach

Federated learning concerns training global models in a decentralized manner. Federated learning is important in many applications, especially when training data come from different sources that cannot be shared with the central server due to restrictions on data sharing. With the increasing capacity of data sources, training samples are usually collected and stored on a regular basis, which leads to an additional issue of sample selection from data sources when one needs to train a global model using the federated learning framework. In this talk, we propose a robust optimization model to incorporate sample selection into global models and develop the robust federated learning framework to train such models.

Orateur: Xuan Vinh Doan (The University of Warwick)

114 Reformulating Chance-Constrained Optimization as Neural Network Learning

Chance-constrained optimization (CCO) problems are stochastic optimization problems with probabilistic constraints defined by a confidence level $\alpha$. A standard solution approach is to transform the CCO problem into a deterministic optimization problem, which is then solved by a numerical solver. However, this approach becomes computationally expensive when dealing with multiple confidence levels, as it requires solving from scratch for each confidence level.
To overcome this inefficiency, we present a deep learning algorithm for efficiently solving the CCO problem over multiple confidence levels. The proposed algorithm can be summarized in the following key steps:
1) Through neurodynamic optimization, we model the CCO problem as an initial value problem (IVP) containing a system of ordinary differential equations.
2) We use physics-informed neural networks (PINNs) to solve that IVP.
3) We use the PINN solution for the confidence level $\alpha^i$ as an initial prediction for the next confidence level $\alpha^{i+1}$, which is improved by retraining the PINN.
Experimental results show that the proposed algorithm provides accurate solutions for the CCO problem at multiple confidence levels, and is significantly more computationally efficient than standard numerical solvers.

Orateur: Dawen WU

Sequential decision-making under uncertainty: Contributed talks

Président de session: Paul Malisani (IFP Energies nouvelles)

115 Solving influence diagrams with MILPs - Recent advances and future directions

An influence diagram is a graph representation of a decision problem that models interdependencies between random events, consequences, and decisions. Recently, two frameworks have been developed to find the optimal decision strategy by transforming the influence diagram into a mixed-integer linear program (MILP). Decision programming (Salo et al., EJOR 299/2, 2022) directly translates the influence diagram into a MILP model, resulting in an exponential number of constraints and variables with respect to the number of nodes in the influence diagram. In contrast, the rooted junction tree framework (Parmentier et al., Informs Journal on Optimization, 2/3, 2020) performs an additional clustering step for the influence diagram before formulating the MILP model. Compared to traditional solution methods, these frameworks offer enormous flexibility in what they can represent through simple modifications to the objective function and constraints. In this presentation, we discuss recent developments related to these frameworks, including new and more efficient reformulations and added modeling flexibility for finding risk-averse decision strategies for influence diagrams. We conclude by presenting our future aspirations for these frameworks to increase the modeling flexibility of influence diagrams as a general framework for structuring and solving sequential decision-making problems involving uncertainty.

Orateur: Topias Terho (Aalto University)

116 Robust stochastic optimization via regularized PHA: Application to Energy Management Systems

This paper deals with robust stochastic optimal control problems. The main contribution is an extension of the Progressive Hedging Algorithm (PHA) that enhances out-of-sample robustness while preserving numerical complexity. This extension involves adopting the widespread practice in machine learning of variance penalization for stochastic optimal control problems. Using the Douglas-Rachford splitting method, the author developed a Regularized Progressive Hedging Algorithm (RPHA) with the same numerical complexity as the standard Progressive Hedging Algorithm (PHA) and improved out-of-sample performance. In addition, the authors propose a three-step control framework consisting of a random scenario generation method, followed by a scenario reduction algorithm, and a scenario-based optimal control computation using the RPHA. Finally, the authors test the proposed method by simulating a stationary battery's Energy Management System (EMS) using ground-truth measurements of electricity consumption and production from a primarily commercial building in Solaize, France. This simulation demonstrates that the proposed method is more efficient than a classical Model Predictive Control (MPC) strategy, which in turn is more efficient than the standard PHA.

Orateur: Paul Malisani (IFP Energies nouvelles)

117 Comparison between different parallelization schemes in SDDP policy training

The Stochastic Dual Dynamic Programming (SDDP) algorithm is widely used to solve multi-stage stochastic problems, such as hydrothermal dispatch in power systems. Due to its iterative nature and the need to handle large volumes of data and multiple future scenarios, SDDP is a computationally intensive method. With the increasing complexity of modern systems and the need to respond to energy market fluctuations and climate variability, computational efficiency in SDDP is a topic of great importance. This study aims to explore different parallelization approaches for the SDDP algorithm to improve its performance in terms of execution time and efficient use of computational resources.

The primary motivation for this research lies in the fact that, despite advancements in processing power, the volume of data and the number of scenarios required for accurate analysis have also grown, creating bottlenecks in the practical application of the algorithm. Thus, investigating parallelization techniques enables the application of SDDP in more complex and dynamic contexts, promoting faster and more reliable responses for energy system operation and planning. The parallelization approaches analyzed include process queue-based parallelization, scenario-based parallelization, and stage-based parallelization. Each approach has specific characteristics that may be advantageous depending on the problem structure and available hardware architecture. All approaches will be compared against serial runs, which use only a single computer core.

For performance analysis, prototypes of the approaches were implemented in a controlled environment using a representative set of hydrothermal dispatch problems. The results on the stability, speed, and reliability of each parallelization scheme will be reported in this study.

The choice of the most suitable parallelization technique depends on several factors, including the number of scenarios, the length of the time horizon, the available hardware architecture, and the memory requirements of the problem. Based on the results, a hybrid approach is recommended for large-scale and complex problems, where scenario-based parallelization and subproblem-based parallelization are combined to maximize efficient use of computational resources. This strategy can provide a robust and efficient solution for hydrothermal dispatch and other applications requiring sequential optimization under uncertainty.

In conclusion, studying different parallelization methods for SDDP is essential to enable its application in large-scale energy systems, where agility and decision accuracy are crucial. This research contributes to advancing performance optimization methods that can be applied not only in the energy sector but also in other areas.

Orateur: Guilherme Bodin (PSR)

Stochastic integer programming: Contributed talks

Président de session: Jeff Linderoth (University of Wisconsin-Madison)

118 Probing-Enhanced Stochastic Programming

We consider a two-stage stochastic decision problem where the decision-maker has the opportunity to obtain information about the distribution of the random variables X through a set of discrete actions that we refer to as probing. Specifically, probing allows the decision-maker to observe components of a random vector Y that is jointly-distributed with X. We propose a three-stage optimization model for this problem, wherein the first-stage variables select components of Y to observe, and decisions in subsequent stages must be consistent with the obtained information. In the case that X and Y have finite support, Goel and Grossmann gave a mixed-integer programming formulation of this problem whose size is proportional to the square of cardinality of the sample space of the random variables. We propose to solve the model using bounds obtained from an information-based relaxation, combined with a branching scheme that enforces the consistency of decisions with observed information. The branch-and-bound approach can naturally be combined with sampling in order to estimate both lower and upper bounds on the optimal solution value. We demonstrate the scalability of our approach against the exact MIP formulation on instances of a stochastic facility location problem.

Orateur: Jeff Linderoth (University of Wisconsin-Madison)

119 Solving a two-stage distributionally robust unit commitment model using Wasserstein distance

The distributionally robust optimization (DRO) framework has emerged as a powerful approach for dealing with uncertainty. In the context of unit commitment, where demand uncertainty affects the right-hand side of constraints, we investigate a DRO approach based on the Wasserstein distance with the $L^2 $-norm. This approach can be addressed using Benders' decomposition as in the risk-neutral approach. However, the key difference lies in the oracle problem that generates valid cuts for the master problem. While the risk-neutral approach requires solving a linear oracle problem at each iteration and for each scenario, the DRO formulation leads to a quadratic convex maximization oracle problem, which has been proven to be NP-hard. Thus, directly solving it with a commercial solver like Gurobi may be inefficient, significantly slowing down Benders' decomposition.

In this talk, we present an efficient solution method for the DRO unit commitment problem, grounded in two key contributions. First, we propose a novel Benders’ reformulation of the stochastic unit commitment that enables faster convergence. Second, we use the Frank-Wolfe algorithm to address the NP-hard oracle subproblem. Finally, numerical experiments assess the efficiency of our approach.

Orateur: Mathis Azéma (CERMICS)

slides_ICSP.pdf

120 Lot-sizing problem under decision-dependent uncertainty: A probing-enhanced stochastic programming approach

We address the Multi-Item Capacitated Lot-Sizing Problem (MCLSP) under decision-dependent uncertainty through a new probing-enhanced stochastic programming framework. In this setting, the demand is strongly correlated with another random vector and the decision-maker can strategically acquire partial information about uncertain demand by selecting component of the correlated random vector to probe, conditioning production decisions on observed covariates. This approach generalizes classical stochastic models by embedding endogenous information acquisition within a three-stage optimization framework. We introduce a compact reformulation that eliminates traditional non-anticipativity constraints, resulting in a stronger linear relaxation and improved computational tractability. We extend classical $(k,U)$ inequalities to the decision-dependent setting and introduce a new class of value-function-based inequalities that strengthen the LP relaxation by capturing the structural relationship between probing and expected recourse costs. These enhancements are embedded within a branch-and-cut algorithm, which also integrates a primal heuristic to accelerate convergence. Computational experiments demonstrate the effectiveness of our proposed methodology. The new formulation together with value-function inequalities consistently outperforms classical approaches, reducing optimality gaps by up to 85%. The full-featured branch-and-cut algorithm achieves optimality gaps below 1.5% on average, even under tight capacity constraints and large scenario sets. These results highlight the critical role of structured reformulation, valid inequalities, and heuristic guidance in solving complex decision-dependent stochastic programs. Our findings display the value of proactive information acquisition and offer scalable tools for production planning under uncertainty.

Orateur: Franco Quezada (Universidad de Santiago de Chile, ENSTA-Paris)

121 Stochastic Revelation in Sequential Decision-Making with a Pharmaceutical Application

In many real-life situations, such as medical product launches, energy investments, or the rollout of new policies, decision-makers must act before knowing exactly when critical information will become available. We develop new mathematical models that incorporate uncertainty about what will happen and when that uncertainty will resolve. Traditional decision-making tools assume fixed timelines for information revelation; instead, we address more realistic scenarios where information arrives at unpredictable moments, making planning more complex and costly if mishandled.

In this talk, we focus on a pharmaceutical application, in particular, the planning and production of medical devices, where firms must be mindful of regulatory approvals. We develop a framework enhanced by problem-specific decomposition methods to address this multistage stochastic problem.

Orateur: Morteza Davari

Mini-symposium: Contextual Stochastic Programming

Présidents de session: Rohit Kannan (Virginia Tech), Utsav Sadana (Université de Montréal)

122 Advances in contextual stochastic optimization for data-driven decision making under uncertainty

Recent advances in operations research (OR) and machine learning (ML) have spurred interest in integrating prediction algorithms with optimization techniques to address decision-making under uncertainty. This has led to the emergence of contextual optimization, a field focused on data-driven methods that prescribe actions based on the most recently available information. These models appear in both OR and ML literature under various names, including data-driven optimization, prescriptive optimization, predictive stochastic programming, policy optimization, (smart) predict-then-optimize, decision-focused learning, and (task-based) end-to-end learning/forecasting/optimization.

In this talk, we will see that these approaches can be unified under the contextual optimization framework. Then, I will discuss some models and methodologies for learning policies from data and the associated challenges.

Orateur: Utsav Sadana (Université de Montréal)

123 Uncertainty Quantification of Decision Performance in Contextual Stochastic Optimization

A fundamental problem in the contextual optimization setting is to evaluate and compare the objective performances of data-driven decision rules. In this regard, we analyze the construction of interval estimates on these performances, as an approach to produce reliable evaluation that handles the underlying statistical uncertainty. Specifically, we systematically compare common plug-in and cross-validation approaches. Despite its wide usage, the statistical benefits of cross-validation approaches have remained half-understood, especially in challenging nonparametric regimes for contextual optimization. In this paper we fill in this gap and show that, in terms of estimating the out-of-sample performances, for a wide spectrum of models, CV does not statistically outperform the simple “plug-in'' approach where one reuses training data for testing evaluation, in terms of both the asymptotic bias and coverage accuracy of the associated interval for out-of-sample evaluation. Our numerical results demonstrate that plug-in performs indeed no worse than CV in estimating decision performance across a wide range of contextual optimization examples.

Orateur: Tianyu Wang

124 Norm-Free Exact Regularization and Applications in Data-Driven Optimization

This paper revisits the theory of \textit{exact regularization} – where optimal solutions of a regularized convex optimization problem exhibit a phase transition phenomenon and eventually coincide with those of the original unregularized problem (under certain conditions).We examine this phenomenon from a norm-free perspective – instead of adopting norm-related assumptions, our results are established on conditions only involving Bregman divergence and convexity. We proved two key results: (1) a norm-free version of Lipschitz continuity of the regularized optimal solution, and (2) a phase-transition threshold for the exact regularization to hold that depends solely on intrinsic problem parameters. Notably, our norm-free framework generalizes classical norm-dependent conditions, such as strong convexity of the regularization function, and broadens applicability. Our theoretical results have applications in many data-driven optimization problems, for example to integrated prediction-optimization, inverse optimization, and decentralized optimization. Our results for exact regularization potentially lead to faster convergence or tighter error bounds in these settings.

Orateur: Meng Qi (Cornell University)

Mini-symposium: Stochastic Mixed-Integer Programming

Président de session: Ward Romeijnders

125 Recent Advances in Solving Multistage Stochastic Mixed-integer Programs

Multistage stochastic mixed-integer programs (MSMIPs) can model complex sequential decision-making problems under uncertainty and appear in many applications. However, due to both the stochastic and integer components, their inherent computational challenges require sophisticated solution methodologies. In this talk, we will review recent advances in solving MSMIPs, in particular for the scenario-tree-based approaches. We will discuss exact methods, bounding ideas, partially extended formulations, and various policy classes, including aggregation-based policies, decision-rule-based policies, and interpretable policies.

Orateur: Dr Merve Bodur (University of Edinburgh)

126 On the ReLU Lagrangian Cuts for Stochastic Mixed Integer Programming

We study stochastic mixed integer programs with both first-stage and recourse decisions involving mixed integer variables. A new family of Lagrangian cuts, termed “ReLU Lagrangian cuts,” is introduced by reformulating the nonanticipativity constraints using ReLU functions. These cuts can be integrated into scenario decomposition methods. We show that including ReLU Lagrangian cuts is sufficient to achieve optimality in the original stochastic mixed integer programs. Without solving the Lagrangian dual problems, we derive closed-form expressions for these cuts. Furthermore, to speed up the cut-generating procedures, we introduce linear programming-based methods to enhance the cut coefficients. Numerical studies demonstrate the effectiveness of the proposed cuts compared to existing cut families.

Orateur: Weijun Xie (Georgia Institute of Technology)

127 Enhanced Lagrangian Cuts for Stochastic Mixed-Integer Programming

This work proposes a globally converging cutting-plane algorithm for solving stochastic mixed-integer programs (SMIP) with general mixed-integer state variables. We show that Lagrangian cuts can approximate the convex envelope of the value function. To approximate the nonconvex value function to exactness, we need to iteratively add binary state variables and generate Lagrangian cuts on the lifted state space. We demonstrate that this lift-and-cut procedure converges to the global optimum asymptotically. However, we show that vanilla Lagrangian cuts can be steep and lead to a poor lower approximation. We propose enhanced Lagrangian cuts, which strengthen the vanilla Lagrangian cut and yield good geometric properties. Extensive computational experiments on the generation expansion planning and security-constrained unit commitment problem demonstrate the effectiveness of our proposed methodology in solving large-scale, multistage stochastic mixed-integer optimization problems.

Orateur: Haoxiang Yang

128 Convex approximations for multistage stochastic mixed-integer programs

We consider multistage stochastic mixed-integer programs. These problems are extremely challenging to solve since the expected cost-to-go functions in these problems are typically non-convex due to the integer decision variables involved. This means that efficient decomposition methods using tools from convex approximations cannot be applied to this problem. For this reason, we construct convex approximations for the expected cost to-go functions and we derive error bounds for these approximations that converge to zero when the total variation of the probability density functions of the random parameters in the model converge to zero. In other words, the convex approximations perform well if the variability of the random parameters in the problem is large enough. To derive these results, we analyze the mixed-integer value functions in the multistage problem, and show that any MILP with convex and Lipschitz continuous objective exhibits asymptotic periodic behavior. Combining these results with total variation bounds on the expectation of periodic functions yields the desired bounds.

Orateur: Ward Romeijnders (University of Groningen)

16:00 Coffee break

Plenary session: Huifu Xu

Président de session: Daniel Kuhn (EPFL)

129 Preference robust optimization

Preference robust optimization (PRO) is a relatively new area of robust optimization. In this talk, I give an overview of recent research on utility-based PRO models and computational methods primarily conducted by my collaborators and myself over the past few years. I begin with a description on one-stage maximin utility PRO model where the true utility function representing the decision maker’s (DM’s) preferences on rewards is ambiguous, discuss how an ambiguity set of utility functions may be constructed based on partially available information, and how such a maximin optimization problem may be efficiently solved. Next, I introduce a multistage PRO model where the DM’s true utility function is historically path dependent and discuss various issues concerning derivation of recursive formulation and numerical solution of the problem via SDDP. One of the main issues to be emphasized is the rectangularity of the ambiguity set of utility functions which underlies the dynamic formulation of the multistage PRO model. To reduce the conservatism of the PRO models, I move on to introduce the main existing approaches which are used to elicit a DM’s preference including relative utility split (RUS) method, random relative utility split (RRUS) method, maximum utility split (RUS) method and polyhedral cut method. These methods are used to design questionnaires for pairwise comparison and subsequently to reduce the size of ambiguity set once a choice is made by the DM. Finally, I extend the discussions to other PRO models including bi-variate utility PRO model, distributionally robust utility preference model when a DM’s preferences are random and PRO models with target/benchmark. The materials of this talk are mostly extracted from my joint papers with Guo and Zhang (2024), Liu and Chen (2025), Zhang, Guo and Sim (2025), Chen and Liu (2025), Haskell and Wu (2025), Hu, Zhnag and Zhang (2024), Wu, Wang and Zhang (2024) as well as other references papers particularly Armbruster and Delage (2015) and Hu and Mehotra (2015).

Orateur: Huifu Xu (The Chinese University of Hong Kong)

130 Sports tournament

mer. 30 juillet

Plenary session: Jim Luedtke

Président de session: David Morton

131 Recent advances in the branch-and-cut approach for solving stochastic integer programs

Stochastic integer programs model problems where discrete decisions must be made under uncertainty. This combination provides significant modeling power, leading to wide a wide variety of applications such as supply chain network design, power systems design and operations, and service systems design and operations. This combination also leads to computational challenges due to the need to consider many possible scenarios of the uncertain parameters and the exponential growth in the solution space associated with the discrete decisions. The branch-and-cut approach for solving this class of problems works by dynamically adding Benders and other cuts derived from considering each scenario independently into a main problem containing the first-stage decision variables. We will review this approach and discuss recent advances, including new techniques for efficiently generating single-scenario cuts. While I will highlight some work in my own group, the presentation will be a broad (but not exhaustive) overview of recent progress on this topic.

Orateur: Jim Luedtke (University of Wisconsin-Madison)

luedtke-icsp-2025.pdf

10:15 Coffee break

Stochastic Programming: Stochastic Optimization in Infinite-Dimensional Spaces

Président de session: Patrick Combettes (North Carolina State University)

132 Stochastic Quasi-Fejér Iterations and Applications

This talk concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which existing solution methods can be recast and improved, and new ones can be designed. Almost sure weak, strong, and linear convergence results are established in particular for fixed point and feasibility problems.

Orateur: Patrick Combettes (North Carolina State University)

133 Inexact JKO and proximal-gradient algorithms in Wasserstein spaces

In this talk, we explore the convergence properties of inexact Jordan-Kinderlehrer-Otto (JKO) schemes and proximal-gradient algorithms in Wasserstein spaces. While the classical JKO scheme assumes exact evaluations at each step, practical implementations rely on approximate solutions due to computational constraints. We analyze two types of inexactness: errors in Wasserstein distance and errors in functional evaluations. We establish rigorous convergence guarantees under controlled error conditions.
Beyond the inexact setting, we also extend the convergence results by considering varying stepsizes. This generalization allows for a broader class of stepsize choices, addressing scenarios where stepsizes evolve dynamically rather than remaining fixed. Our analysis expands previous approaches, providing new insights into discrete Wasserstein gradient flows. These findings contribute to the theoretical understanding of approximate optimization methods in Wasserstein spaces, with possible implications for applications into sampling, PDEs and machine learning.

Orateur: Emanuele Naldi (Università degli studi di Genova)

134 An Improved Analysis of the Clipped Stochastic subGradient Method under Heavy-Tailed Noise

In this talk, we show novel optimal (or near optimal) convergence rates for a clipped version of the projected stochastic subgradient method. We consider nonsmooth convex problems in Hilbert spaces over possibly unbounded domains, under heavy-tailed noise that possesses only the first $p$ moments for $p \in \left]1,2\right]$. For the last iterate, we establish convergence in expectation with rates of order $(\log^{1/p} k)/k^{(p-1)/p}$ and $1/k^{(p-1)/p}$ for infinite and finite-horizon respectively. We also derive new convergence rates, in expectation and with high probability, for the average iterate --- improving the state of the art. Those results are applied to the problem of supervised learning with kernels demonstrating the effectiveness of our theory. Finally, we give preliminary experiments.

Orateur: Saverio Salzo (Sapienza Università di Roma)

135 Block-Activated Algorithms for Multi-Stage Variational Inequalities

We discuss an approach for designing block-activated algorithms for solving the monotone multi-stage stochastic variational inequalities in extensive form proposed by Rockafellar and Wets. Advantages over the classical progressive hedging algorithm will be discussed.

Orateur: Minh Bui (Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz)

(Distributionally) Robust Optimization: Contributed talks

Président de session: Eojin Han (University of Notre Dame)

136 Robust chance-constrained optimization with discrete distributions via a bundle approach

Typically, probability distributions that generate uncertain parameters are uncertain themselves or even unknown. Distributional robustness determines optimized decisions that are protected in a robust fashion against all probability distributions in some appropriately chosen ambiguity set. We consider robust joint chance-constrained optimization problems with discrete probability distributions and introduce a practically efficient scenario-based bundle method without convexity assumptions on the constraint functions. We start by deriving an approximation problem to the original robust chance-constrained version by using smoothing and penalization techniques. The scenario-based bundle method first solves the approximation problem with a classical bundle method, and then uses the bundle solution to decide which scenarios to include in a scenario-expanded formulation. In our numerical experiments we demonstrate the efficiency of our approach on real-world gas transport problems with uncertain demands. Comparing our results to the classical robust reformulations for ambiguity sets consisting of confidence intervals and Wasserstein balls, we observe that the scenario-based bundle method often outperforms solving the classical reformulation directly and is guaranteed to find feasible solutions.

Orateur: Daniela Bernhard (Friedrich-Alexander Universität Erlangen-Nürnberg)

presentation.pdf

137 Nonlinear Decision Rules Made Scalable by Nonparametric Liftings

Sequential decision making often requires dynamic policies, which are computationally not tractable in general. Decision rules provide approximate solutions by restricting decisions to simple functions of uncertainties. In this paper, we consider a nonparametric lifting framework where the uncertainty space is lifted to higher dimensions to obtain nonlinear decision rules. Current lifting-based approaches require predetermined functions and are parametric. We propose two nonparametric liftings, which derive the nonlinear functions by leveraging the uncertainty set structure and problem coefficients. Both methods integrate the benefits from lifting and nonparametric approaches, and hence provide scalable decision rules with performance bounds. More specifically, the set-driven lifting is constructed by finding polyhedrons within uncertainty sets, inducing piecewise-linear decision rules with performance bounds. The dynamics-driven lifting, on the other hand, is constructed by extracting geometric information and accounting for problem coefficients. This is achieved by using linear decision rules of the original problem, also enabling one to quantify lower bounds of objective improvements over linear decision rules. Numerical comparisons with competing methods demonstrate superior computational scalability and comparable performance in objectives. These observations are magnified in multistage problems with extended time horizons, suggesting practical applicability of the proposed nonparametric liftings in large-scale dynamic robust optimization.

Orateur: Eojin Han (University of Notre Dame)

138 Data-driven interdiction with asymmetric cost uncertainty: a distributionally robust optimization approach

We consider a class of stochastic interdiction games between an upper-level decision-maker (referred to as a leader) and a lower-level decision-maker (referred to as a follower), where the follower's objective function coefficients are subject to uncertainty.
More specifically, unlike traditional deterministic interdiction problem settings, the follower's profits (or costs) in our model comprise a random vector, whose probability distribution is estimated independently by the leader and by the follower, based on their own data. In order to address the distributional uncertainty, we formulate a Wasserstein distributionally robust interdiction (DRI) problem, where both decision-makers attempt to hedge against the worst-case distributions and realizations of the follower's objective function coefficients. If the leader has full information about the follower's data, then the DRI problem with properly defined Wasserstein ambiguity sets and objective criteria is shown to admit a single-level mixed-integer linear programming (MILP) reformulation of polynomial size. In contrast, when the leader has incomplete or no information about the follower’s data, we propose two distinct approaches for approximating the DRI problem. The first approach employs a pessimistic approximation, which turns out to be computationally challenging and requires the design of a specialized Benders decomposition algorithm. The second approach leverages a finite set of candidate data sets that satisfy prescribed interval constraints and addresses the resulting problem via a one, potentially large single-level MILP reformulation. Finally, for a class of randomly generated instances of the packing interdiction problem, we evaluate numerically how the information asymmetry and the decision-makers' risk preferences affect the model's out-of-sample performance.

Orateur: Sergei Ketkov (Department of Business Administration, University of Zurich)

Presentation.pdf

139 Fixed Interval Scheduling with Random Delays: Distributionally Robust and Multi-stage Approaches

In logistics and transportation, scheduling tasks with fixed start times is a common challenge, often complicated by unpredictable delays. To tackle these issues, we need robust optimization techniques that can adapt to real-world uncertainties.
Initially, we explore an operational FIS problem where job completion times are influenced by random delays, modeled using Archimedean copulas to capture known dependencies. We aim to maximize the worst-case probability that a schedule remains feasible under stress conditions affecting some marginal delay distributions. By reformulating the problem, we connect it to established risk measures, paving the way for efficient solutions through decomposition.
The second strategy involves a dynamic framework that allows for job reassignment at key decision points, responding to observed delays. This creates a complex mixed-integer stochastic program, requiring novel methods to simplify and solve.
A practical application for these models is the gate assignment problem at airports, where flights must be allocated to gates while considering arrival delay uncertainties. The diverse compatibility between aircraft and gates, along with the ability to adjust assignments over time, makes this an intriguing case study. We provide computational results for the initial problem and discuss methodological progress and future prospects for the latter.

Orateur: Monika Matoušková

Application in energy, finance or logistics: Contributed talks

Président de session: Lars Hellemo (SINTEF)

140 Stochastic Programming for the Green Transition: Model Composition and Decomposition

The green transition poses many challenges following the introduction of renewable energy sources (RES) and sector coupling (e.g. integrating heat and power). Decision makers need to apply more complex models and to better account for uncertainty, often stemming from the non-dispatchable nature of important RES.

While solution techniques for stochastic programs are available and demonstated in academia, many hurdles slow the application of these in day-to-day analyses, as both models and algorithms are hard modify, and require significant tailoring to each new application or model to benefit from theoretical advances.
We propose a modular approach to modelling, facilitating the composition of different model components to cover a wide range of temporal and geographical scales, as well as different formulations for technology descriptions.

In particular, by semantically encoding the time structure of a problem, using a utility library (TimeStruct), we not only formulate complex time structures with ease, but also allow analysts to construct models with compatible time structures to enable linking of models.

Decomposition techniques can be applied to existing models by linking models providing a node-based interface to build generic decomposition on top of other models (see e.g. Plasmo).

In contrast, we propose exploiting the already encoded time structure to enable automatic decomposition based on TimeStruct and develop algorithms that can be applied across multiple models that build on this library.
We demonstrate automatically applying Benders decomposition based on the encoded time structure on optimization models from different domains:

1. Developing zero emission energy systems in the Arctic
2. Composing green product portfolios in the fertilizer industry

Orateur: Lars Hellemo (SINTEF)

2025-07-30_ICSP_Hellemo.pdf

141 Multicut Benders Decomposition for Generation Expansion with Dynamic Probabilistic Reserves

This study implements and compares single and multicut Benders decomposition (BD) for the generation expansion problem (GEP) involving numerous renewable energy plants, incorporating Time-Varying Dynamic Probabilistic Reserve (DPR). We first identify the conditions under which the second stage (operation problem) of the GEP is convex. However, even when the resulting problem is convex, the incorporation of DPR introduces complexity to the optimization process, which justifies the investigation of enhanced forms of BD.

DPR is computed by considering the forecast error of non-dispatchable renewable generation between consecutive hours. The forecast error accounts for the renewable generation at each hour for each scenario and day within the relevant horizon. It is defined using a convex combination of the expected value and the Conditional Value at Risk (CVAR) of the absolute value of the forecast error between consecutive hours. We show that this function is convex, and since it only appears on the Right-Hand side (RHS) of the reserve requirement constraint, the resulting second stage is convex.

Unlike most BD applications, the bottleneck in each iteration of solving a GEP lies in the second stage, which requires using Stochastic Dual Dynamic Programming (SDDP). Solving this stage takes significantly longer than the first stage, a small mixed-integer programming (MIP) problem. Therefore, implementing a multicut strategy in the first stage is particularly advantageous, as it trades a slight increase in the complexity of an easier subproblem for a decrease in BD iterations and, consequently, the number of second-stage solves.

Orateur: Tiago Andrade (PSR)

icsp2025_TiagoAndrade.pdf

142 Learning Data-Driven Uncertainty Set Partitions for Robust and Adaptive Energy Forecasting with Missing Data

Short-term forecasting models typically assume the availability of input data (features) when they are deployed and in use. However, equipment failures, disruptions, and cyberattacks may lead to missing features when such models are used operationally, which could negatively affect forecast accuracy and result in suboptimal operational decisions. In this paper, we use adaptive robust optimization and adversarial machine learning to develop forecasting models that seamlessly handle missing data operationally. We propose linear- and neural network-based forecasting models with parameters that adapt to available features, combining linear adaptation with a novel algorithm for learning data-driven uncertainty set partitions. The proposed adaptive models do not rely on identifying historical missing data patterns and are suitable for real-time operations under stringent time constraints. Extensive numerical experiments on short-term wind power forecasting considering horizons from 15 minutes to 4 hours ahead illustrate that our proposed adaptive models are on par with imputation when data are missing for very short periods (e.g., when only the latest measurement is missing) whereas they significantly outperform imputation when data are missing for longer periods. We further provide insights by showcasing how linear adaptation and data-driven partitions
(even with a few subsets) approach the performance of the optimal, yet impractical, method of retraining for every possible realization of missing data.

Orateur: Akylas Stratigakos (Imperial College London)

143 Stochastic Programming for Renewable Energy Procurement with Targets

In recent years, many companies have committed to renewable energy procurement targets, which usually require a certain fraction of the annual demand to be met by renewables. This annual approach overlooks the temporal fluctuations in energy supply and demand, leading to a growing interest in 24/7 targets that aim to match every consumed kilo-watt hour with carbon-free electricity sources at every hour of every day. Since this target is difficult to meet in real life, two relaxations can be defined: (i) hourly target, requiring a minimum fraction of demand to be met by renewables every hour; and (ii) temporal target, ensuring that the demand is fully covered by renewables for a specified fraction of the hours.

In this study we present a two-stage stochastic programming model to optimize procurement decisions to meet a target, using a combination of solar and wind power purchase agreements (PPAs), energy attribute certificates (EACs), and energy storage. In the first stage, decisions on PPA and storage sizes are made; in the second stage, these assets, alongside EACs, are used to meet demand and renewable targets throughout the planning horizon. Future electricity demand, renewable supply, and market prices of electricity and EACs are all uncertain factors that affect procurement decisions.

To tackle this stochastic program, we first demonstrate analytically that no target type between hourly and temporal dominates the other in terms of cost-efficiency. Then, including a discrete set of demand and price scenarios, we solve a two-stage mixed-integer linear programming formulation of our problem both by a commercial solver and scenario decomposition techniques. Preliminary numerical results reveal variations in procurement decisions when we relax the target fraction, distinguishing between hourly and temporal targets. Moreover, by incorporating different demand profiles (i.e., mostly flat, seasonal, and peaky), we highlight the necessity of transitioning from an annual matching framework to a 24/7 one, aiding the companies to set and meet renewable energy targets.

Orateur: Gülin Yurter (University of Twente)

Yurter_Gulin_ICSP25_Static.pdf

YurterGulin_ICSP25_ppt.pptx

Chance-constrained programming: Chance constraints in optimal control II

Président de session: René Henrion (WIAS Berlin)

144 Time-optimal control under chance constraints

Time optimal control is a classical problem in control theory.
In the case that the initial state is known exactly, the problem is to find a feasible control that steers the system exactly to the prescribed target state as fast as possible. For systems where the initial state is uncertain, the statement of the problem has to be modified to take into account this uncertainty. We replace the exact target condition by the condition that a certain norm of the difference of the actual final state and the desired target state is less than a given value epsilon with a probability that is larger than a prescribed parameter p. In this way we prescribe a probabilistic terminal condition. We are looking for a control such that this chance-constraint is satisfied as fast as possible.

Orateur: Prof. Martin Gugat (FAU Erlangen)

145 An enumerative formula for the spherical cap discrepancy

The spherical cap discrepancy is a widely used measure for how uniformly a sample of points on the sphere is distributed. It is particularly important for estimating the integration error for certain classes of functions on the sphere. Being hard to compute, this discrepancy measure is typically replaced by some lower or upper estimates when designing optimal sampling schemes for the uniform distribution on the sphere. A fully explicit, easy to implement enumerative formula for the spherical cap discrepancy is provided. This formula is of combinatorial nature and, thus, its application is limited to spheres of small dimension and moderate sample sizes. It could be shown that the cap discrepancy is Lipschitz continuous in a neighbourhood of so-called generic point sets. This property may have some impact on optimal quantization, i.e., on finding point sets of fixed size on the sphere having minimum spherical discrepancy.

Orateur: Holger Heitsch (WIAS Berlin)

146 Optimal control of elliptic PDEs with joint chance state constraints

We study optimal control of PDEs under uncertainty with the state variable subject to joint chance constraints. These constraints ensure that the random state variable meets pointwise bounds with high probability. For linear governing PDEs and elliptically distributed random parameters, we prove existence and uniqueness results for almost-everywhere state bounds. We prove variance reduction properties for the spherical-radial decomposition compared to the standard Monte Carlo estimator. We discuss different expansions of the uncertain variable in the governing equation. Numerical examples for linear and bilinear PDEs compare the performance of Monte Carlo and quasi-Monte Carlo sampling methods. We also study how the accuracy of the probabilities depends on the truncation of the random variable expansion, and numerically illustrate the variance reduction of the SRD. Finally, we discuss variants of the proposed algorithms for Gaussian process regression.

Orateur: Georg Stadler (Courant Institute, New York University)

147 Optimal control of polyhedral sweeping processes with chance constraint

Sweeping processe have been introduced by J.J. Moreau in 1971. These are special differential inclusions where the set-valued right-hand side is represented by the normal cone to some moving set. We consider the optimal control of polyhedral sweeping processe subject to a terminal state constraint. We shall assume that the control is affected by a random perturbation so that the terminal state constraint becomes random too. This leads us to formulate a chance constraint, namely that the terminal state constraint be satisfied with some given high probability. The talk presents several structural results about such sweeping processes (well-posedness, existence of solutions) as well as algorithmic solution approaches.

Orateur: René Henrion

ML: Machine Learning and Off-Policy Learning Robust Distribution Shifts

Président de session: Phebe Vayanos (University of Southern California)

148 Mixed-feature Logistic Regression Robust to Distribution Shifts

Logistic regression models are widely used in the social and behavioral sciences and in high-stakes domains, due to their simplicity and interpretability properties. At the same time, such domains are permeated by distribution shifts, where the distribution generating the data changes between training and deployment. In this paper, we study a distributionally robust logistic regression problem that seeks the model that will perform best against adversarial realizations of the data distribution drawn from a suitably constructed Wasserstein ambiguity set. Our model and solution approach differ from prior work in that we can capture settings where the likelihood of distribution shifts can vary across features, significantly broadening the applicability of our model relative to the state-of-the-art. We propose a graph-based solution approach that can be integrated into off-the-shelf optimization solvers. We evaluate the performance of our model and algorithms on numerous publicly available datasets. Our solution achieves a 408x speed-up relative to the state-of-the-art. Additionally, compared to the state-of-the-art, our model reduces average calibration error by up to 36.19% and worst-case calibration error by up to 41.70%, while increasing the average area under the ROC curve (AUC) by up to 18.02% and worst-case AUC by up to 48.37%.

Orateur: Prof. Phebe Vayanos (University of Southern California)

149 Learning optimal prescriptive trees robust to distribution shifts

In domains such as personalized medicine, historical data is used to learn what treatments to prescribe to maximize positive outcomes. Previous studies have proposed methods for creating prescriptive trees: human-interpretable diagrams that indicate what type of treatment an individual should get based on their measurements. However, a remaining problem is that the models perform worse over time when there is a shift in the data collection process or when data from a different source is used during the training and prediction phases. To solve this problem, we propose a method that considers data uncertainty by optimizing distributionally robust prescriptive trees. We formulate a linear-time algorithm to find the worst-case distribution shift within a given Wasserstein distance around the dataset and use it as a subroutine within the main problem. Our algorithm does not depend on any specific causal effect estimator and can, therefore, be applied in various contexts.

Orateur: Daniël Vos (Delft University of Technology)

150 Learning Optimal Classification Trees Robust to Distribution Shifts

We consider the problem of learning classification trees that are robust to distribution shifts between training and testing/deployment data. This problem arises frequently in high stakes settings such as public health and social work where data is often collected using self-reported surveys which are highly sensitive to e.g., the framing of the questions, the time when and place where the survey is conducted, and the level of comfort the interviewee has in sharing information with the interviewer. We propose a method for learning optimal robust classification trees based on mixed-integer robust optimization technology. In particular, we demonstrate that the problem of learning an optimal robust tree can be cast as a single-stage mixed-integer robust optimization problem with a highly nonlinear and discontinuous objective. We reformulate this problem equivalently as a two-stage linear robust optimization problem for which we devise a tailored solution procedure based on constraint generation. We evaluate the performance of our approach on numerous publicly available datasets, and compare the performance to a regularized, non-robust optimal tree. We show an increase of up to 12.48% in worst-case accuracy and of up to 4.85% in average-case accuracy across several datasets and distribution shifts from using our robust solution in comparison to the non-robust one.

Orateur: Nathan Justin (University of Southern California)

151 Inexact Column Generation for Causal Discovery

Causal structure learning, the task of inferring causal relationships from data, is computationally challenging due to its combinatorial nature. State-of-the-art integer programming formulations suffer from exponential growth in the number of variables and constraints, while traditional column generation approaches struggle with the complexity of solving mixed-integer nonlinear programming pricing problems. In this talk, we propose an inexact column generation method that reformulates the pricing problem as a difference of submodular minimization problem. This approach significantly reduces the computational complexity of pricing subproblems while maintaining the quality of generated columns. Empirical results demonstrate that our method outperforms pure integer programming approaches, such as GOBNILP, in both solution quality and computational efficiency.

Orateur: Rui Chen (Chinese University of Hong Kong, Shenzhen)

Sequential decision-making under uncertainty: Contributed talks

Président de session: David Wozabal (Vrije Universiteit Amsterdam)

152 Lagrange Duality Gap of Decomposed Dynamic Programming: The Case of Bandits

This study explores multi-armed bandit problems under the premise that the decision-maker possesses prior knowledge of the arms' distributions and knows the finite time horizon. These conditions render the problems suitable for stochastic multistage optimization decomposition techniques. On the one hand, multi-armed bandit algorithms are integral to reinforcement learning and are supported by extensive theoretical analysis, particularly regarding regret minimization. Meanwhile, stochastic multistage optimization emphasizes examining the performance gap between a given policy and the optimal, adapted policy, which can be estimated numerically through dual methods. Within this framework, decomposition strategies have been demonstrated to efficiently tackle large-scale stochastic multistage optimization challenges. A fact in dire need of better theoretical understanding. On the empirical side, our experiments corroborate the approach's efficacy on multi-armed bandit. On the theoretical side, we reinterpret the duality gap by relating it to quantities defined along the trajectory of the decision-making process: the Lagrangian multiplier, the instantaneous reward and the value of information. This lays the groundwork for subsequent investigations into the performance of decomposition methods.

Orateur: Benjamin Heymann

153 A Comparative Study of Sampling-based Multistage Stochastic Linear Programming Algorithms

Multistage stochastic linear programming (MSLP) offers a powerful framework for decision-making under uncertainty over time. Sampling-based algorithms provide a practical approach to solving the MSLP problems, particularly in large-scale settings. In this arena, stochastic dual dynamic programming (SDDP) has proven to be very effective. SDDP utilizes randomization to solve a deterministic representation, such as a sample average approximation, of an MSLP problem. In contrast, stochastic dynamic linear programming (SDLP) is an internal sampling algorithm that operates on a dynamically evolving representation of an MSLP, using sequentially generated sample paths. In this talk, we present a comparative study of these two prominent sampling-based approaches for solving stagewise independent MSLP problems. We also present a regularized variant of SDDP that, like SDLP, employs a basic feasible policy to identify the prox-center. We evaluate the algorithms on benchmark instances of varying sizes and structures, assessing their convergence behavior and computational efficiency. A series of numerical experiments is conducted to demonstrate the trade-offs among these methods in terms of accuracy and scalability.

Orateur: Harsha Gangammanavar (Southern Methodist University)

154 Optimal Information Relaxation Bounds for Multi-Stage Stochastic Optimization

This paper addresses the computation of tight optimistic bounds for multi-stage stochastic optimization problems using information relaxation duality. We introduce a specific class of penalty functions—bi-linear in decisions and the innovations of the underlying stochastic process—to penalize anticipative policies. Our approach provides a generic framework for deriving such bounds, notably without requiring explicit knowledge or approximation of the problem's value functions. We formulate a minimax problem to find the optimal penalty parameters within this specific class, yielding the tightest bound achievable with these penalties. We show that for convex problems, this minimax problem can be equivalently reformulated as a standard stochastic program with expectation constraints. Furthermore, we propose an iterative algorithm to solve the minimax problem directly. The methodology offers a computationally tractable approach to generate bounds that are stronger than simple perfect information relaxations, thereby improving the evaluation of heuristic policies.

Orateur: David Wozabal (Vrije Universiteit Amsterdam)

155 A Two-Timescale Primal-Dual Framework for Reinforcement Learning via Online Dual Variable Guidance

We study reinforcement learning by combining recent advances in regularized linear programming formulations with the classical theory of stochastic approximation.
Motivated by the challenge of designing algorithms that leverage off-policy data while maintaining on-policy exploration, we propose PGDA-RL, a novel primal-dual Projected Gradient Descent-Ascent algorithm for solving regularized Markov Decision Processes (MDPs). PGDA-RL integrates experience replay-based gradient estimation with a two-timescale decomposition of the underlying nested optimization problem.
The algorithm operates asynchronously, interacts with the environment through a single trajectory of correlated data, and updates its policy online in response to the dual variable associated with the occupation measure of the underlying MDP. We prove that PGDA-RL converges almost surely to the optimal value function and policy of the regularized MDP. Our convergence analysis relies on tools from stochastic approximation theory and holds under weaker assumptions than those required by existing primal-dual RL approaches, notably removing the need for a simulator or a fixed behavioral policy.

Orateur: Axel Friedrich Wolter (University of Konstanz)

Wolter_Presentation_ICSP2025.pdf

Mini-symposium: Junior Researcher Prize

Président de session: Wim van Ackooij (EDF Lab Paris-Saclay)

156 A nonparametric algorithm for optimal stopping based on robust optimization

Optimal stopping is a fundamental class of stochastic dynamic optimization problems with numerous applications in finance and operations management. We introduce a new approach for solving computationally-demanding stochastic optimal stopping problems with known probability distributions. The approach uses simulation to construct a robust optimization problem that approximates the stochastic optimal stopping problem to any arbitrary accuracy; we then solve the robust optimization problem to obtain near-optimal Markovian stopping rules for the stochastic optimal stopping problem.

In this work, we focus on designing algorithms for solving the robust optimization problems that approximate the stochastic optimal stopping problems. These robust optimization problems are challenging to solve because they require optimizing over the infinite-dimensional space of all Markovian stopping rules. We overcome this challenge by characterizing the structure of optimal Markovian stopping rules for the robust optimization problems. In particular, we show that optimal Markovian stopping rules for the robust optimization problems have a structure that is surprisingly simple and finite-dimensional. We leverage this structure to develop an exact reformulation of the robust optimization problem as a zero-one bilinear program over totally unimodular constraints. We show that the bilinear program can be solved in polynomial time in special cases, establish computational complexity results for general cases, and develop polynomial-time heuristics by relating the bilinear program to the maximal closure problem from graph theory. Numerical experiments demonstrate that our algorithms for solving the robust optimization problems are practical and can outperform state-of-the-art simulation-based algorithms in the context of widely-studied stochastic optimal stopping problems from high-dimensional option pricing.

Orateur: Bradley Sturt (University of Illinois Chicago)

157 Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionality

Wasserstein distributionally robust optimization (DRO) aims to find robust and generalizable solutions by hedging against data perturbations in Wasserstein distance. Despite its recent empirical success in operations research and machine learning, existing performance guarantees for generic loss functions are either overly conservative because of the curse of dimensionality or plausible only in large sample asymptotics. In this paper, we develop a nonasymptotic framework for analyzing the out-of-sample performance for Wasserstein robust learning and the generalization bound for its related Lipschitz and gradient regularization problems. To the best of our knowledge, this gives the first finite-sample guarantee for generic Wasserstein DRO problems without suffering from the curse of dimensionality. Our results highlight that Wasserstein DRO, with a properly chosen radius, balances between the empirical mean of the loss and the variation of the loss, measured by the Lipschitz norm or the gradient norm of the loss. Our analysis is based on two novel methodological developments that are of independent interest: (1) a new concentration inequality controlling the decay rate of large deviation probabilities by the variation of the loss and (2) a localized Rademacher complexity theory based on the variation of the loss.

Orateur: Dr Rui Gao (UT Austin)

Mini-symposium: Modeling flexibility: new developments

158 Stochastic programming as a learning tool

Much of the stochastic programming literature is on mathematics or algorithms, some is on principal models. But very few are on real use of the models. I discuss the problems that arise when trying to really use stochastic programming, and where I think we are (or should be) headed.

Orateur: Prof. Stein W. Wallace (NHH Norwegian School of Economics)

159 Modeling multistage uncertainty with Time Series Foundation Models and Doob decomposition

Time Series Foundation Models, like ChatGPT for language, are trained on vast amounts of curated time series data and can produce a sequence of high-quality predictions from a single input sequence. Can we apply Time Series Foundation Models to the challenge of generating multistage scenario trees?

This talk explores a method based on Doob's observation that every discrete-time stochastic process is equal to the sum of a predictive process and a martingale. It is a natural idea to use Time Series Foundation Models for the predictive part. The missing piece, of course, is the martingale.

Martingale ideas are a well-known part of the stochastic programming playbook. They underpin the progressive hedging algorithm of Rockafellar and Wets, and in options pricing problems (real and financial) the optimal dual solution is related to a martingale.

This talk presents some basic principles and some experiments into the construction of martingales from time series data, and the coupling of the martingale to a TSFM-generated predictive process. Finally, for the problem of evaluating options for flexibility, it may turn out that constructing martingales is actually a solution algorithm.

Orateur: Alan King (IBM Research)

160 Enhancing Flexibility in Stochastic Programming with Neural Networks

Flexibility is a critical attribute in solving stochastic programming problems, where decision-making must account for uncertainty and adapt to a wide range of potential future scenarios. Stochastic programming is a practical approach in which decisions are determined prior to the realization of uncertain variables, with subsequent adjustments made through recourse mechanisms once the uncertainties are revealed. Traditional solving methods rely on scenario-based approximations, where incorporating additional scenarios may improve accuracy but simultaneously escalates computational complexity, often making large-scale problems computationally intractable.
This study aims to address these challenges by using neural networks as surrogate models to estimate solution quality across diverse scenarios, thereby reducing the computational burden when integrated into the optimization framework. Empirical evaluations have been conducted on single-source capacitated Facility Location Problems, a stochastic variation of the multi-path Traveling Salesman Problem. Preliminary results demonstrate the effectiveness of this approach taking advantage of the generalization capability of the neural network model.

Orateur: Enza Messina (University of Milano-Bicocca)

Mini-symposium: Robust Decision Making in Dynamic Environments

Président de session: Mengmeng Li (EPFL)

161 Estimation and Prediction Procedures for Unified Robust Decision Models

Over the past two decades, robust optimization techniques have efficiently addressed decision problems under uncertainty, offering high assurance of feasibility without being overly conservative. However, research on estimating parameters for robust decision models from data is relatively scarce. In this paper, we focus on a unified framework for robust decision models that integrate robust optimization and robust satisficing paradigms. In particular, we identify two layers of uncertainty: outcome uncertainty, involving deviations from specified inputs based on historical data, and estimation uncertainty, addressing deviations from latent input vectors (such as the unobservable true mean). We introduce estimation and prediction procedures tailored to reduce conservativeness while enhancing feasibility within this unified robust decision framework. Specifically, we introduce the concept of a minimum volume confidence set that minimizes the size of the outcome confidence set while considering the likelihood of infeasibility, thereby improving the precision of uncertainty characterization. This method also accommodates asymmetric uncertainty. Moreover, our framework incorporates an affine predictive model that leverages side information to improve input vector predictions, seamlessly integrating into robust decision models. Our method has been implemented in the algebraic modeling toolbox, RSOME, facilitating practical applications.

Orateur: Melvyn Sim (NUS Business School)

162 Towards Optimal Offline Reinforcement Learning

We study offline reinforcement learning problems with a long-run average reward objective. The state-action pairs generated by any fixed behavioral policy thus follow a Markov chain, and the empirical state-action-next-state distribution satisfies a large deviations principle. We use the rate function of this large deviations principle to construct an uncertainty set for the unknown true state-action-next-state distribution. We also construct a distribution shift transformation that maps any distribution in this uncertainty set to a state-action-next-state distribution of the Markov chain generated by a fixed evaluation policy, which may differ from the unknown behavioral policy. We prove that the worst-case average reward of the evaluation policy with respect to all distributions in the shifted uncertainty set provides, in a rigorous statistical sense, the least conservative estimator for the average reward under the unknown true distribution. This guarantee is available even if one has only access to one single trajectory of serially correlated state-action pairs. The emerging robust optimization problem can be viewed as a robust Markov decision process with a non-rectangular uncertainty set. We adapt an efficient policy gradient algorithm to solve this problem. Numerical experiments show that our methods compare favorably against state-of-the-art methods.

Orateur: Mengmeng Li (EPFL)

163 Episodic Bayesian Optimal Control with Unknown Randomness Distributions

Stochastic optimal control with unknown randomness distributions has been studied for a long time, encompassing robust control, distributionally robust control, and adaptive control. We propose a new episodic Bayesian approach that incorporates Bayesian learning with optimal control. In each episode, the approach learns the randomness distribution with a Bayesian posterior and subsequently solves the corresponding Bayesian average estimate of the true problem. The resulting policy is exercised during the episode, while additional data/observations of the randomness are collected to update the Bayesian posterior for the next episode. We show that the resulting episodic value functions and policies converge almost surely to their optimal counterparts of the true problem if the parametrized model of the randomness distribution is correctly specified. With an approximation commonly used in statistical analysis, we further show that the asymptotic convergence rate of the episodic value functions is of the order $O(N^{-1/2})$, where $N$ is the number of episodes given that only one data point is collected in each episode. We develop an efficient computational method based on stochastic dual dynamic programming (SDDP) for a class of problems that   have convex cost functions and linear state dynamics. Our numerical results on a classical inventory control problem verify the theoretical convergence results, and numerical comparison with two other methods demonstrate the effectiveness of the proposed Bayesian approach.

Orateur: Enlu Zhou

164 Learning Uncertainty Sets in Dynamic Robust Optimization

We present a data-driven technique to automatically learn uncertainty sets in dynamic decision making under uncertainty. We formulate the learning problem as a control design problem where the control policy involves solving a robust optimization problem parametrized by the past disturbances, as well as the parameters of the uncertainty set. We propose a learning procedure to dynamically predict the parameters of the uncertainty set to minimize a closed-loop performance metric while satisfying probabilistic guarantees of constraint satisfaction. Our approach allows for uncertain data that is correlated across time periods, and can learn a wide range of commonly used uncertainty sets. By modeling our training problem objective and constraints using coherent risk metrics, we derive finite sample probabilistic guarantees of constraint satisfaction in multi-stage settings.

Orateur: Irina Wang (Princeton University)

12:45 Lunch

13:30 Excursion to Château de Fontainebleau

jeu. 31 juillet

Plenary session: Francesca Maggioni

Président de session: Guzin Bayraksan (The Ohio State University)

165 Bounding Large Scale Optimization Problems under Uncertainty

Many real world decision problems are dynamic and affected by uncertainty. Stochastic Programming provides a powerful approach to handle this uncertainty within a multi-period decision framework. However, as the number of stages increases, the computational complexity of these problems grows exponentially, posing significant challenges. To tackle this, approximation techniques are often used to simplify the original problem, providing useful upper and lower bounds for the objective function’s optimal value.
This talk explores methods for generating bounds for a wide variety of problem structures affected by uncertainty. We begin by discussing bounds based on scenario grouping under the assumption that a sufficiently large scenario tree is given but is unsolvable, both in the context of stochastic programming and distributionally robust optimization. Next, we extend these techniques to address more complex problems, including multi-horizon stochastic optimization.
Finally, the talk introduces the integration of these bounding methods with Benders’ decomposition. A Benders refinement-chain cuts method is proposed, where scenario subsets are used to generate group-wise optimality cuts. This aggregation significantly lowers the number of cuts required, while preserving valid lower bounds. Theoretical relationships between cuts generated at different refinement levels are established.
Numerical experiments on various energy and transportation optimization problems demonstrate the efficiency of the proposed approaches.

Orateur: Francesca Maggioni (Department of Management, Information and Production Engineering, University of Bergamo)

ICSP2025_Parigi_NEW.pdf

10:15 Coffee break

Stochastic Programming

Président de session: Bernardo Freitas Paulo da Costa (Fundação Getulio Vargas)

166 An stochastic differential equation perspective on stochastic convex optimization

We analyze the global and local behavior of gradient-like flows under stochastic errors towards the aim of solving convex optimization problems with noisy gradient input. We first study the unconstrained differentiable convex case, using a stochastic differential equation where the drift term is minus the gradient of the objective function and the diffusion term is either bounded or square-integrable. In this context, under Lipschitz continuity of the gradient, our first main result shows almost sure convergence of the objective and the trajectory process towards a minimizer of the objective function. We also provide a comprehensive complexity analysis by establishing several new pointwise and ergodic convergence rates in expectation for the convex, strongly convex, and (local) Łojasiewicz case. The latter, which involves local analysis, is challenging and requires non-trivial arguments from measure theory. Then, we extend our study to the constrained case and more generally to certain nonsmooth situations. We show that several of our results have natural extensions obtained by replacing the gradient of the objective function by a cocoercive monotone operator. This makes it possible to obtain similar convergence results for optimization problems with an additively "smooth + non-smooth" convex structure. Finally, we consider another extension of our results to non-smooth optimization which is based on the Moreau envelope.

Orateur: Rodrigo Maulen Soto

167 Value functions in LinearDecisionRules.jl

The use of linear decision rules is an attractive alternative to multistage decision making under uncertainty, combining simplicity and interpretability of the policies and computational tractability. We introduce a modeling extension to the LinearDecisionRules.jl package that allows the user to formulate and optimize value functions in this framework. The extension also simplifies incorporating such value functions as convex formulations to be used in further optimization problems.

Orateur: Bernardo Freitas Paulo da Costa (Fundação Getulio Vargas)

Bernardo_VF_LDR_ICSP_2025.pdf

168 A Stochastic Linear Tracing Procedure to Select a Proper Markov Perfect Equilibrium in Stochastic Games

The linear tracing procedure plays an essential role in Harsanyi and Selten's (1988) equilibrium selection theory. The concept of proper equilibrium was formulated by Myerson (1978), which is able to eliminate some counterintuitive perfect equilibria in normal-form games. An extension of proper equilibrium to stochastic games leads to a notion of proper Markov perfect equilibrium. To select such an equilibrium, this paper develops a stochastic linear tracing procedure through the constitution of a perturbed stochastic game in which each player in each state maximizes her payoff against a linear convex combination between a prior belief profile and a given mixed stationary strategy profile, where the combination coefficient for each player in each state is a function given by an extra variable to the power of the number of pure actions for the player in each state. Applying the optimality conditions to the integration of the perturbed stochastic game and a convex-quadratic-penalty game, we acquire from the equilibrium condition and transformations on variables a smooth path that starts from an arbitrary Markov strategy profile and ends at a proper Markov perfect equilibrium. As an alternative scheme for the equilibrium selection, we present a stochastic logarithmic tracing procedure to approximate the stochastic linear tracing procedure for selecting a proper Markov perfect equilibrium. Moreover, we give a stochastic linear tracing procedure and a stochastic logarithmic tracing procedure for selecting a perfect d-proper Markov perfect equilibrium, which provides an approximate proper Markov perfect equilibrium but is much less costly to compute.

Orateur: Chuangyin Dang (City University of Hong Kong)

Stochastic Programming: Contributed Talks

169 A Stochastic Newton-type Method for Non-smooth Optimization

We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (approximation) of the Hessian. We derive, using a variant of Chernoff bounds for stopping times, expectation and probability bounds for the random variable representing the number of iterations of the algorithm until approximate first order optimality conditions are validated. As an important distinction to previous results in the literature, we do not require that the estimator is unbiased or that it has finite variance. We then showcase our theoretical results in a stochastic Quasi-Newton method for X-ray free electron laser orbital tomography and in a sketched Newton method for image denoising.

Orateur: Titus Pinta (ENSTA)

170 Sampling the Optimal Solution of an Optimization Problem with Random Parameters

We present a novel method for sampling the optimal solution of unconstrained, strictly convex optimization problems with random parameters. The motivating application are methods in two-
stage stochastic programming, which often rely on computing (the expectation of) optimal dual variables for linear programs with random coefficients.

Conventional methods typically proceed by generating samples of the parameters and then solving the optimization problem for each individual realization. By contrast, we directly generate samples of the optimal solution by simulating an appropriately chosen diffusion process adapted to the target distribution, while implementing a metropolis correction step to improve numerical stability.

We present preliminary numerical results for the case where the random optimization problem is a log-barrier regularization of a linear program, and the simulated diffusion process is a version of the Metropolis Adjusted Langevin Algorithm (MALA).

Orateur: Jonathan Hornewall (École Des Ponts)

171 Stochastic Optimization with Optimal Importance Sampling

Importance Sampling (IS) is a widely used variance reduction technique for enhancing the efficiency of Monte Carlo methods, particularly in rare-event simulation and related applications. Despite its power, the performance of IS is often highly sensitive to the choice of the proposal distribution and frequently requires stochastic calibration techniques. While the design and analysis of IS have been extensively studied in estimation settings, applying IS within stochastic optimization introduces a unique challenge: the decision and the IS distribution are mutually dependent, creating a circular optimization structure. This interdependence complicates both the analysis of convergence for decision iterates and the efficiency of the IS scheme. In this paper, we propose an iterative gradient-based algorithm that jointly updates the decision variable and the IS distribution without requiring time-scale separation between the two. Our method achieves the lowest possible asymptotic variance and guarantees global convergence under convexity of the objective and mild assumptions on the IS distribution family. Furthermore, we show that these properties are preserved under linear constraints by incorporating a recent variant of Nesterov’s dual averaging method.

Orateur: Dr Liviu Aolaritei (UC Berkeley)

Application in energy, finance or logistics: Contributed talks

Président de session: André Diniz (CEPEL/UERJ)

172 Optimal Operation and Valuation of Electricity Storages

We apply computational techniques of convex stochastic optimization to optimal operation and valuation of electricity storages in the face of uncertain electricity prices. Our approach is applicable to various specifications of storages, and it allows for e.g. hard constraints on storage capacity and charging speed. Our valuations are based on the indifference pricing principle, which builds on optimal trading strategies and calibrates to the user's initial position, market views and risk preferences. We illustrate the effects of storage capacity and charging speed by numerically computing the valuations using stochastic dual dynamic programming.

Orateur: François Pacaud (Mines Paris - PSL)

173 INTERMODAL SERVICE ASSESSMENT USING THE MARKOV DECISION PROCESS: A CASE STUDY OF BRAZIL’S FERROGRAO RAILROAD PROJECT

Decision support models are essential for assessing logistics infrastructure projects, such as intermodal terminals. This study proposes a methodology to analyze the multiple impacts of strategic decisions on terminal location in conjunction with the tactical problem of designing an intermodal service. The case study of Mato Grosso’s soybean export logistics network was structured as a Markov Decision Process (MDP) and resolved through a backward induction algorithm, which solves the single-source shortest-path problem. The application of the proposed methodology, called ISA-MDP, to the upcoming EF-170 (“Ferrogrão”) railroad project has identified the economic, social, and environmental impacts of constructing a new railway and intermodal terminal on the contestable and captive hinterlands of each logistics export corridor. Due to changes in hinterlands and the cargo attraction potential of the new terminal, resulting in shifts in transportation traffic flow, logistics costs are estimated to reduce by up to $16 per ton, while greenhouse gas emissions are expected to decrease by approximately 35% through shifts in transportation modes. However, since the project is situated within the Amazon and Cerrado biomes, the potential benefits must be contrasted to land use changes driven by anthropic activities. These include the occupation of indigenous territories, direct deforestation caused by the railroad installation, and indirect deforestation caused by soybean croplands expansion process towards conservation areas. This process aggravates the effects of climate change, which are not adequately addressed in the project's Environmental Impact Assessment (EIA).

Orateur: João Marcelo Leal Gomes Leite (Universidade de São Paulo (USP))

ICSP2025 - Intermodal Service Assessment.pdf

174 Renewable Energy Communities with Peer-to-Peer Exchange: a chance-constraint approach

This work presents a chance-constraint model for the management of Energy
Communities, focusing on prosumers and peer-to-peer electricity exchanges.

The model aims to minimize the total operation costs of the community, while ensuring
energy balance and satisfying technical constraints related to local production and the
energy exchanges both inside the community and with the main grid.

Uncertainty in solar photovoltaic generation and electricity demand is addressed using
individual and joint chance constraints that are modeled using normal distributions and
approximated through piecewise-linear techniques when necessary. 

The model is tested on a prototype example of community and is implemented in Python
using Pyomo.

Orateur: M. Santo Saraceno (University of Brescia)

175 A Combined Branch‑and‑Cut and Two‑Stage Benders Decomposition for the Stochastic Day‑Ahead Hydrothermal Unit Commitment Problem

The increasing penetration of wind and solar generation amplifies the uncertainty in the short term unit commitment problem for hydrothermal power systems, challenging, for example, schedules that are given by deterministic approaches, as is the case of the day ahead-unit commitment model (DESSEM) used for the official dispatch and price setting of the Brazilian system, over a seven day horizon. Such model employs a mixed integer linear programming approach (MILP), with some ad-hoc accelerating techniques. In this work a combined Branch and cut/ two stage Benders decomposition approach is proposed to consider uncertainties in that model, while trying to minimize deviations to the standard deterministic plan. The second stage subproblems capture the deviations in the scheduling of the first day, through a compact scenario set for renewable generation. The subproblem for each scenario is solved as a linear program with recourse, whose dual information generates Benders optimality cuts that are inserted “on the fly” as lazy constraints during the master Branch and Bound search, in a scheme labeled as “Branch and Benders Cut”. Preliminary tests on a simplified representative instance indicate that the stochastic layer introduces only a moderate computational burden while yielding a more reliable treatment of uncertainty and, consequently, smoother and more realistic energy price signals. Therefore, the formulation offers a practical and economically pathway for incorporating renewable variability and uncertainty into an industrial software for hydrothermal unit commitment, without causing a disruptive change in existing operational workflows for running the model by the Brazilian institutions.

Keywords: two stage stochastic programming; Branch and Benders Cut; hydrothermal unit commitment; renewable uncertainty; energy price formation.

Orateur: André Diniz (CEPEL/UERJ)

Contextual stochastic programming

Président de session: Tito Homem-de-Mello (Universidad Adolfo Ibáñez)

176 Application-Driven Optimal Pointwise Forecasts for a Class of Two-Stage Stochastic Programs

We consider the class of two-stage stochastic programs with uncertainty only on the right-hand side. Such a class encompasses practical many problems, especially in inventory models. We show that, under certain conditions, there exist an optimal scenario, in the sense that solving the problem with that scenario yields the same optimal solution as the original problem. In the case data-driven problems with contextual information, the result means that pointwise forecasts of the uncertain variables can be optimal. While such a scenario---which does not have be unique---is usually unknown, we present an integrated learning and optimization procedure that yields the best approximation of that scenario within the modeler's pre-specified set of parameterized forecast functions. Numerical results conducted with inventory problems from the literature as well as a microgrid energy management problem with real data demonstrate that the proposed approach performs well when compared to benchmark methods.

Orateur: Tito Homem-de-Mello (Universidad Adolfo Ibáñez)

177 Data-Driven Distributionally Robust Contextual Optimization with Gaussian Mixture Models

We study contextual stochastic optimization problems in which the joint distribution of uncertain parameters and side information covariates is modeled as a mixture of Gaussians. In a data-driven setting, the parameters of this distribution are unknown and must be estimated from historical data. To mitigate the adverse effects of estimation errors and improve out-of-sample performance, we propose a distributionally robust optimization framework based on the Kullback–Leibler divergence. We show that centering the ambiguity set at the empirical conditional distribution, rather than the joint distribution, is crucial for ensuring meaningful solutions. We derive a finite-sample out-of-sample performance guarantee and prove that the optimal KL divergence radius scales at the same rate as the statistical learning rate of the estimated parameters, up to constant factors. We further develop an efficient solution scheme based on exponential conic programming and demonstrate the superior empirical performance of our method compared to existing approaches across several real-world contextual optimization settings.

Orateur: Grani Adiwena Hanasusanto (University of Illinois Urbana-Champaign)

178 Contextual Distributionally Robust Optimization under Streaming Data: An Alternating Optimization Method

We consider data-driven decision-making that incorporates a prediction model within the 1-Wasserstein distributionally robust optimization (DRO) given joint observations of uncertain parameters and covariates using regression residuals in a streaming-data setting. In this setting, additional data becomes available and allows decisions to adapt to the growing knowledge of the underlying uncertainty. The ambiguity set shrinks as more data is observed. We propose an efficient online optimization method for this streaming-data contextual DRO setting, which iteratively alternates between optimizing the decision and determining the worst-case distribution. We analyze the asymptotic convergence properties of this algorithm and establish dynamic regret bounds to certify the performance of online solutions. Through numerical experiments, we validate our theoretical findings and demonstrate that our approach significantly enhances computational efficiency while maintaining high solution quality under streaming data.

Orateur: Guzin Bayraksan (The Ohio State University)

179 Optimize, then Predict

This paper proposes an Optimize-then-Predict framework in which we identify the optimal decision before predicting or observing the realized values. The optimization part can be run in low-demand environments, saving computational time during runtime. We also propose computationally efficient inferences for the evaluation of model performance.

This paper shows that in any optimization problem, the expected loss always equals the covariance between the optimal decision and the decision variables, such as costs. The decision variables may be known or unknown at the time the optimal decision is made. However, the expected loss can be estimated in advance from historical or even simulated data.

This paper also derives an ex ante optimal closed-form solution for any predict-then-optimize problem. In addition, the paper shows that in expectation, predict-then-optimize problems are equivalent to optimize-then-predict problems. Empirical experiments on the shortest path algorithm verify the claims in the paper.

Orateur: Irene Aldridge (Cornell University, Cambridge University)

ML: Exploring the synergy between stochastic optimization, dynamics, sampling, inference, and optimal transport I

Président de session: Jia-Jie Zhu (Weierstrass Institute, Berlin)

180 Score Learning under the Manifold Hypothesis: Theory and Implications for Data Science

The score function plays a central role in modern generative modeling, particularly in diffusion models and related score-based methods. Despite its theoretical appeal, learning the score function in practice is notoriously difficult: it is sensitive to hyperparameter choices and prone to various forms of instability that often require ad hoc corrections.

In this talk, we study score learning under the popular manifold hypothesis, which posits that high-dimensional data concentrates near a low-dimensional manifold. A key and perhaps surprising insight is that, under this hypothesis, it is significantly easier to learn the underlying manifold structure than the full data distribution. We provide theoretical support for this claim and explore its consequences for score estimation and generative modeling. In particular, we show how this perspective can clarify challenges in training diffusion models and guide the development of more stable and efficient algorithms.

Orateur: Ya-Ping Hsieh (ETH Zürich)

181 A stochastic optimal transport approach to unstable free boundary problems

The supercooled Stefan problem describes freezing of supercooled water. In contrast to the Stefan problem that describes melting of ice, the supercooled problem exhibits unstable behaviour which makes the usual PDE methods break down. We will discuss some recent progress which employs a stochastic version of optimal transport, involving optimal stopping times of the Brownian motion.

Orateur: Young-Heon Kim (University of British Columbia)

182 Contrasting and combining Wasserstein and Fisher-Rao flows for relative entropy minimization

Many problems in machine learning can be framed as variational problems that minimize the relative entropy between two probability measures. Many recent works have exploited the connection between the (Otto-)Wasserstein gradient flow of the Kullback-–Leibler (KL) divergence and various sampling, Bayesian inference, and generative modeling algorithms. In this talk, I will first contrast the Wasserstein flow with the Fisher-Rao flows of those divergences, and showcase their distinct analysis properties when working with different relative entropy driving energies, including the reverse and forward KL divergence. Building upon recent advances in the mathematical foundation of the Hellinger-Kantorovich (HK, a.k.a. Wasserstein-Fisher-Rao) gradient flows, I will then show the analysis of the HK flows and its implications for computational algorithms for machine learning and optimization.

Orateur: Jia-Jie Zhu (Weierstrass Institute, Berlin)

Sequential decision-making under uncertainty: Contributed talks

Président de session: Hoda Bidkhori (George Mason University)

183 S&P 500 optimal investing based on SDDP and implied calibrated ARIMA-GARCH model

An implied distribution of the underlying asset price for the options expiration moment can be obtained from the market option prices [1]. However, exchange-traded options rarely expire more often than once a month. It is not enough for planning dynamic decisions in many cases. In [2] implied calibration of the dynamic ARMA(1,1)-GARCH(1,1) model using market prices of options of different expirations is considered. We use historical data from the S&P 500 index options for the numerical experiments. The parameters of the risk-neutral model are chosen in such a way that the sum of squares of the relative mistakes in option prices was minimal. During this process, model prices of options are calculated using the Monte-Carlo method. To solve the corresponding problem of optimal calibration, the Randomized Stochastic Projected Gradient Free Method [3] is used. The theorem regarding the conditions of convergence of the algorithm is given in this paper. We proved that the conditions of the theorem are satisfied for our case. Thus, the algorithm converges for our problem of ARMA(1,1)-GARCH(1,1) calibration. Then, the corresponding physical ARMA-GARCH version is obtained according to [4].
This physical ARMA(1,1)-GARCH(1,1) model is used to construct a scenario lattice as described in [5]. The problem of the position in S&P 500 management for the SDDP algorithm is formulated. The results of the historical simulation are also presented in the report.

References
1. D.T. Breeden and R.H. Litzenberger (1978). Prices of State-Contingent Claims Implicit in Option Prices, Journal of Business, Vol. 51, pp. 621–51.
2. P. Arbuzov, D. Golembiovskii. Calibration of underlying asset ARIMA-GARCH model based on market option prices, Economics and Mathematical Methods, expected to be published in the third quarter of 2025. (In Russian).
3. S. Ghadimi, G. Lan, H. Zhang (2013). Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimization, https://arxiv.org/abs/1308.6594 .
4. R. Bliss and N. Panigirtzoglou (2004). Recovering risk aversion from options, Journal of Finance, Vol. 59, pp. 407-446.
5. D. Golembiovsky, A. Pavlov, D. Smetanin (2021). Experimental Study of Methods of Scenario Lattice Construction for Stochastic Dual Dynamic Programming, Open Journal of Optimization, Vol.10 No.2, pp. 47-60.

Orateur: Dmitrii Golembiovskii (Moscow State University named Lomonosov)

184 Chemotherapy Outpatient Scheduling Optimization with a Practical Application Luxembourg

Cancer is the second leading cause of death in the world. Unfortunately, the projections from the International Agency for Research on Cancer (IARC) indicate a rising trend for new cancer cases in the following years. Among the various cancer treatments, chemotherapy is one of the most effective treatments for numerous cancer types. It generally contains one or more prescribed molecules according to a tailored protocol to eliminate or inhibit the growth of cancer cells. In recent years, chemotherapy outpatient scheduling has emerged as a critical and complex research topic due to the rising number of patients, the uncertainties in treatment processes, resource constraints, and the interdependencies between the sequential stages of treatment. The chemotherapy process generally includes the following steps: patient admission, blood testing, oncologist evaluation and validation, molecule production, infusion (or injection), and discharge. Numerous uncertainties are associated with the chemotherapy treatment process. For instance, our numerical analysis shows significant dispersion in molecule production times, even for identical molecules. In this research, we develop optimization models that account for these uncertainties across the different stages of the chemotherapy treatment process. Our objective is to enhance responsiveness to rising demand, reduce patient waiting times, and improve resource utilization. We evaluate our approach using data from a chemotherapy clinic in Luxembourg.

Orateur: Nihat Oner (University of Luxembourg)

185 Computing Usage Values for Prospective Studies in Energy Systems Using Spatial Decomposition

The increasing penetration of renewable energy sources in power systems amplifies the need for storage to manage their inherent intermittency. In this context, evaluating the opportunity cost of stored energy—commonly referred to as usage values—becomes essential. These values can be computed by solving a multistage stochastic optimization problem, where uncertainty arises from net demand (the aggregation of consumption and non-dispatchable generation), the availability of dispatchable units, and inflows for hydroelectric storage.

We aim to compute these usage values for each country in the interconnected European electrical system in the context of the prospective studies currently carried out by RTE using their simulation tool, Antares. The energy system is mathematically modeled as an oriented graph, where nodes represent countries and arcs represent interconnection links. The combination of spatial complexity (50 nodes, one storage per node) and temporal complexity (a one-year horizon modeled at two timescales—weeks and hours) makes the application of classical stochastic dynamic programming techniques, such as SDDP, challenging.

To address this, we apply Dual Approximate Dynamic Programming (DADP), which decomposes the global multistage stochastic optimization problem into smaller independent nodal problems and a transport problem. This decomposition produces nodal usage values that depend only on the local state, independently of the states of other nodes.

To assess the accuracy of this approach, we present a case study involving three countries—France, Germany, and Switzerland—each modeled with a representative energy mix, a single storage unit, and a few dispatchable generators. Interconnections between countries are modeled as aggregated exchange links between countries. For this tractable model, we compute the exact usage values as functions of the three storages, and benchmark them against the approximations produced by decomposition methods under varying approximation levels.

Finally, we present numerical results illustrating the behavior of the DADP algorithm in this two-timescale setting, where usage values are computed at the weekly scale, while decomposition prices are computed at the hourly scale.

Orateur: Camila Martinez Parra (RTE-France)

186 Robust Quickest Change Detection in Non-Stationary Processes

Exactly and asymptotically optimal algorithms are developed for robust detection of changes in non-stationary processes. In non-stationary processes, the distribution of the data after change varies with time. The decision maker does not have access to precise information on the post-change distribution. It is shown that if the post-change non-stationary family has a distribution that is least favorable in a well-defined sense, then the algorithms designed using the least favorable laws are robust optimal. This is the first result where an exactly robust optimal solution is obtained in a non-stationary setting, where the least favorable law is also allowed to be non-stationary. Examples of non-stationary processes encountered in public health monitoring and space and military applications are provided. Our robust algorithms are also applied to real and simulated data to show their effectiveness.

Orateur: Hoda Bidkhori (George Mason University)

Mini-symposium: Computationally Efficient Approaches for Distributionally Robust Optimization

Président de session: JIANQIANG CHENG (University of Arizona)

187 Simple Yet Effective Approximations for Optimization under Uncertainty

This talk focus on developing computationally efficient approximations for solving optimization problem under uncertainty. We first present a novel and simple modeling method called harmonizing optimization (HO), which integrates SAA and DRO with moment by adaptively adjusting the weights of data and information based on sample size N. This allows HO to amplify data effects in large samples while emphasizing information in smaller ones. More importantly, HO performs well across varying data sizes without needing to classify them as large or small. We provide practical methods for determining these weights and demonstrate that HO offers finite-sample performance guarantee. Moreover, to solve HO efficiently, we propose an optimized dimensionality reduction approach by integrating the dimensionality reduction of random parameters with the subsequent optimization problems. As an application, HO can be used to enhance scenario reduction by retaining critical information from reduced scenarios, thereby improving approximation quality and reducing completion time. Numerical results show significant advantages of HO in solution quality compared to other benchmark approaches, and highlight its effectiveness in scenario reduction.

Orateur: JIANQIANG CHENG (University of Arizona)

188 The Value of Stochastic Solutions in Adaptive Decision-Making

We revisit the value of stochastic solutions (VSS) in adaptive stochastic optimization. Given a fixed decision, VSS evaluates its suboptimality in contrast to an optimal solution with knowledge of the underlying probability distribution. For example, for a decision given by the sample average approximation (SAA), VSS interprets the value of collecting more data for better decision-making. When the distributional knowledge is ambiguous, VSS is uncomputable and we propose best-case VSS (VSSB) and worst-case VSS (VSSW) to provide a confidence interval. Specifically, we use a Wasserstein ball to model the ambiguity and show that this confidence interval shrinks linearly as the ball radius diminishes to zero. In addition, we derive tractable and conservative approximations for VSSB and VSSW through Lagrangian relaxation, and further improve these approximations through conjugate duality. Notably, the error bounds for these approximations are also linear in the ball radius. Finally, using the newsvendor and the production-transportation problems, we demonstrate the small VSS of the SAA decisions in contrast to other popular decision-making paradigms and the effectiveness of the proposed approximations.

Orateur: Ruiwei Jiang (University of Michigan)

189 Distributionally Robust Optimization with Multimodal Decision-Dependent Ambiguity Sets

We consider a two-stage distributionally robust optimization (DRO) model with multimodal uncertainty, where both the mode probabilities and uncertainty distributions could be affected by the first-stage decisions. To address this setting, we propose a generic framework by introducing a ϕ-divergence based ambiguity set to characterize the decision-dependent mode probabilities and further consider both moment-based and Wasserstein distance-based ambiguity sets to characterize the uncertainty distribution under each mode. We identify two special ϕ-divergence examples (variation distance and χ2-distance) and provide specific forms of decision dependence relationships under which we can derive tractable reformulations. Furthermore, we investigate the
benefits of considering multimodality in a DRO model compared to a single-modal counterpart through an analytical analysis. Additionally, we develop a separation-based decomposition algorithm to solve the resulting multimodal decision-dependent DRO models with finite convergence and optimality guarantee under certain settings. We provide a detailed computational study over two example problem settings, the facility location problem and shipment planning problem with pricing, to illustrate our results, which demonstrate that omission of multimodality and decision-dependent uncertainties within DRO frameworks result in inadequately performing solutions with worse in-sample and out-of-sample performances under various settings. We further demonstrate the speed-ups obtained by the solution algorithm against the off-the-shelf
solver over various instances.

Orateur: Beste Basciftci (University of Iowa)

Mini-symposium: Decomposition methods for solving Stochastic Programming problems in Logistics and Transportation

Présidents de session: Daniele Manerba (Università degli Studi di Brescia), Francesca Maggioni (Department of Management, Information and Production Engineering, University of Bergamo)

190 Stochastic programming in freight transportation: connecting theory and practice.

Freight transportation is one of the critical enablers of trade, both global and domestic. Given that, it regularly constitutes significant portions of the gross domestic product of countries. Due to its large scale, small percentage improvements in the efficiency of freight transportation operations can lead to large monetary savings as well as reduced environmental impacts. At the same time, freight transportation operations are fraught with uncertainty, making reliably achieving high levels of efficiency a challenge. The purpose of this talk is to illustrate how stochastic programming has, and can, effectively impact the planning of freight transportation operations. To do so, the talk will be divided into three parts. In the first, we will discuss the sources and types of uncertainty that impact freight operations in practice. In the second, we will review the classical optimization models that have been proposed to support the planning of freight transportation operations. We will also discuss when and how those classical models can accommodate the natures and types of uncertainty experienced in practical freight transportation operations. In the third, we will discuss new research on a stochastic program for effectively matching supply and demand that recognizes the different customer segments for freight transportation in practice. We will also present a decomposition-based solution method for solving large-scale instances of that model.

Orateur: Mike Hewitt (Loyola University Chicago)

191 Progressive Hedging-based approach for combined forward and reverse logistics in hub-and-spoke e-commerce networks

A consolidated business model for managing e-commerce logistics involves the combination of forward-and-reverse operations, where the collection of returns is ensured along with the distribution of products, and the use of hub-and-spoke networks, in which both distribution and collection demand from many customers are aggregated into intermediate hubs. In this context, we study a complex variant of the Vehicle Routing Problem with divisible deliveries and pickups, in which each hub may be associated with a mandatory delivery demand and a mandatory return pickup demand, and it may be visited more than once within the same or different routes. Given the large fluctuation of demand within the aggregating hubs, we also assume that an uncertain optional pickup quantity may arise and propose a two-stage Stochastic Programming formulation including ad-hoc recourse actions. The difficulty of solving the resulting model over many scenarios is overcome by the development of a Progressive Hedging-based matheuristic approach exploiting a scenario-wise problem decomposition, an Augmented Lagrangian Relaxation convergence framework, as well as heuristic improvements and refinements. Our method outperforms state-of-the-art solvers in terms of quality of the solution and efficiency over a representative set of realistic instances for the problem at hand and can be easily adapted to other similar settings.

Orateur: Daniele Manerba (Università degli Studi di Brescia)

192 A Benders decomposition approach for a green bi-objective stochastic fleet size and composition vehicle routing problem.

In this study, we examine the optimization of fleet size and mix, together with vehicle routing, under uncertain demand conditions, with explicit consideration of sustainability aspects in the context of Last Mile logistics. We propose a two-stage bi-objective stochastic mixed-integer programming model that simultaneously minimizes total costs and vehicle emissions associated with delivery activities. The first-stage tactical decisions involve determining the fleet size, composition, and consistent routing, whereas the second-stage operational decisions pertain to the allocation of parcels to be delivered and the selection of customers to be served by an external delivery provider. The ε-constraint method is applied to transform the bi-objective problem into a single-objective formulation, enabling the identification of all Pareto-optimal solutions. To cope with the computational challenges posed by real-world instances, an L-shaped algorithm is designed and implemented within the ε-constraint framework. The performance of the L-shaped approach is evaluated, demonstrating that it provides cost-effective solutions in short computational time. Managerial insights are finally discussed.

Orateur: Paolo Beatrici (University of Bergamo)

193 Incorporating decision-dependent demand uncertainty in mobility pricing: a carsharing case

The problem of pricing mobility services has attracted significant attention. In most studies, uncertain demand is modeled as an exogenous random variable with known distribution. This assumption overlooks the likely effect of prices on user adoption decisions. To address this dependency, we formulate the pricing problem as a stochastic program with decision-dependent demand uncertainty. Specifically, we make the non-standard assumption that the distribution of demand depends on pricing decisions. We show that the problem can be written as an extensive mixed-integer linear program whose size is exponential in the input parameters. To find numerical solutions we devise a specialized exact decomposition method. The method builds on distribution-specific cuts for the generation of which we prove closed-form primal and dual solutions to the necessary sub-problems. Extensive numerical experiments on a one-way carsharing system operating in Copenhagen, Denmark, demonstrate that taking into account the effect of prices on uncertain demand increases the expected profits by 4.91% compared to a benchmark considering deterministic price-elastic demand. Service rates are likewise high, corresponding to 93.37% on expectation. Furthermore, we show that the solution method outperforms by far a commercial solver used to solve the monolithic formulation, hereby extending the domain of practically tractable problems. While the focus of the paper is on carsharing services, we comment on how the proposed modeling and solution strategy naturally extends to many types of mobility pricing problems.

Orateur: Jiali Deng

Mini-symposium: Stochastic Optimization under Decision-Dependent Uncertainty

Président de session: Giovanni Pantuso (University of Copenhagen)

194 Stochastic Optimization with Decision-Dependent Uncertainty: A Tour D'Horizon

In this talk we provide an introduction to stochastic optimization problems with decision-dependent uncertainty.
We review the main lines of research in terms of both methodology and applications.
Our discussion will center on a taxonomy of these problems, distinguishing between uncertainties that affect probabilities (Type 1) and those that influence resolution time (Type 2). Additionally, we will explore problem structures such as decision stages, underlying assumptions, and solution approaches.
We will conclude with an overview of the main challenges in this field and propose future research directions.

Orateur: Giovanni Pantuso (University of Copenhagen)

195 Distributionally Robust Chance-Constrained Optimization with Decision-Dependent Support

We study distributionally robust chance-constrained optimization problems under decision-dependent uncertainty. The focus is on decision-dependent uncertainty of Type 1 in which the support of the random variables is decision-dependent. We study various types of coupling functions and ambiguity. We derive computationally tractable equivalent reformulations and design customized solution methods, whose effectiveness is illustrated with a series of computational tests.

Orateur: Miguel Lejeune (George Washington University)

196 Residuals-Based Contextual Distributionally Robust Optimization with Decision-Dependent Uncertainty

We consider a residuals-based distributionally robust optimization model, where the underlying uncertainty depends on both covariate information and our decisions. We adopt regression models to learn the latent decision dependency and construct a nominal distribution (thereby ambiguity sets) around the learned model using empirical residuals from the regressions. Ambiguity sets can be formed via the Wasserstein distance, a sample robust approach, or with the same support as the nominal empirical distribution (e.g., phi-divergences), where both the nominal distribution and the radii of the ambiguity sets could be decision- and covariate-dependent. We provide conditions under which desired statistical properties, such as asymptotic optimality, rates of convergence, and finite sample guarantees, are satisfied. Via cross-validation, we devise data-driven approaches to find the best radii for different ambiguity sets, which can be decision-(in)dependent and covariate-(in)dependent. Through numerical experiments, we illustrate the effectiveness of our approach and the benefits of integrating decision dependency into a residuals-based DRO framework.

Orateur: Xian Yu (The Ohio State University)

197 Exact and Approximate Schemes for Robust Optimization Problems with Decision-Dependent Information Discovery

In uncertain optimization problems with decision-dependent information discovery, the decision-maker can influence when information is revealed, unlike the classic setting where uncertain parameters are revealed according to a prescribed filtration. This work examines two-stage robust optimization problems with decision-dependent information discovery, focusing on uncertainty in the objective function. We introduce the first exact algorithm for this class of problems and enhance the existing K-adaptability approximation by strengthening its formulation. Our approaches are tested on robust orienteering and shortest-path problems. We study the interplay between information and adaptability, demonstrating that the exact solution method often outperforms the K-adaptability approximation. Moreover, our experiments highlight the benefits of the strengthened K-adaptability formulation over the classical one, even in settings with decision-independent information discovery.

Orateur: Rosario Paradiso (Vrije Universiteit Amsterdam)

12:45 Lunch

198 EWGSO Board meeting

Memorial session: Memorial session dedicated to Werner Romisch and J-B Wets

Présidents de session: Johannes Royset (University of Southern California), René Henrion

SPS Business Meeting: News, discussions and election of new COSP members

Président de session: Phebe Vayanos (University of Southern California)

Gala Dinner: Dinner at Hotel Pullman Bercy - Subway M14 - Cour St Emilion

ven. 1 août

Plenary session: Erick Delage

Président de session: Claudia Sagastizábal

199 Reinforcement Learning Methods for Risk-Sensitive Sequential Decision Making

This talk surveys recent developments in reinforcement learning (RL) methods for risk-aware model-free decision-making in Markov decision processes (MDPs). In the discounted setting, we adapt two popular risk neutral RL methods to account for risk aversion. The first approach minimizes a dynamic utility-based shortfall risk measure, while the other optimizes a specific quantile of the total discounted cost. We then present an RL framework for average-cost MDPs that incorporates dynamic risk measures. Together, these contributions represent a significant step toward scalable, risk-aware, model-free, sequential decision-making methods. The presentation will highlight the theoretical motivations, convergence guarantees, and empirical performance of these algorithms, offering insights into their applicability in finance and beyond.

Orateur: Erick Delage (HEC Montréal)

ICSP_talk5.pdf

10:15 Coffee break

Stochastic Programming: Contributed talks

Président de session: Claudia Sagastizábal

200 Linear Convergence in Bundle Progressive Hedging and its link to Proximal Decomposition

Progressive Hedging and Proximal Decomposition are popular splitting methods for large-scale stochastic optimization. We present a formal equivalence between Progressive Hedging and Proximal Decomposition when the nonanticipativity constraint is a subspace, as well as a result of linear convergence of their bundle versions under standard error-bound assumptions once an infinite null-step tail appears—a situation for which convergence rates in bundle methods have not been analyzed previously.

Joint work with Felipe Atenas, Claudia Sagastizábal and Mikhail Solodov

Orateur: Théo Molfessis (École Polytechnique)

ICSP_presentation_Molfessis.pdf

201 Expanding the reach of progressive hedging methods

Many popular splitting methods for large-scale stochastic optimization are derived from Spingarn's partial inverse framework. Well-known and popular methods such as Progressive Hedging and Proximal Decomposition are paradigmatic examples of this class. We present lessons learned by examining Spingarn's framework from a dual perspective, inspired from bundle methods in nonsmooth optimization.

Joint work with Felipe Atenas, Theo Molfessis and Mikhail Solodov

Orateur: Dr Claudia Sagastizábal (IMECC)

202 Stability of stochastic programs specified by distortion risk measures with the application in the game theory

In this paper, we deal with the stability of stochastic programming problems that are specified by distortion risk measures. The distortion risk measure is a specific type of risk functional that is defined as the Choquet integral of a random variable with respect to distorted probability measure. The distortion of the probability measure is governed by a distortion function that encodes the agent's "distorted perception" of the true probability measure. Distortion risk measures characterize risk functionals that are monotone with respect to first-order stochastic dominance. This class of risk measures covers most of the commonly used risk measures, in particular, all coherent risk measures are distortion risk measures. The stability of stochastic programming problems has been in great extent covered by the work of Werner Römish. Our goal is to extend this work to stochastic programs that are specified in terms of some distortion risk measures. The main results of this paper are qualitative and quantitative conditions for the stability of such programs. We formulate these conditions in terms of program-canonical distances on the sets of probability measures, but we also show the conditions for the stability with respect to risk-neutral version of these distances that correspond to distances used by Römish. We apply these results to the problem of finding generalized equilibria in the model of a game with random payoff.

Orateur: Lukáš Račko (Charles university)

203 Approximations of Rockafellians, Lagrangians, and Duals in Stochastic Programming Problems

In stochastic programming, solutions are highly sensitive to approximations—whether from sampling, scenario reduction, or parametric perturbations—especially in nonconvex settings. This work investigates how substitute problems, constructed via Rockafellian functions, can provide robustness against such stochastic approximations. Unlike classical stability analysis centered on local perturbations near (local) minimizers, we employ epi-convergence to assess whether approximating problems, derived from stochastic perturbations, converge globally to the true problem. We demonstrate that, under natural assumptions, these substitute problems exhibit well-behaved epi-convergence even when the original stochastic program does not. Furthermore, we quantify convergence rates, which often translate to Lipschitz-type stability for optimal values and solutions under stochastic perturbations. Our framework bridges Rockafellian relaxation techniques with stochastic programming, offering new tools for analyzing robustness in data-driven or distributionally uncertain settings.

Orateur: Julio Deride (Universidad Adolfo Ibáñez)

(Distributionally) Robust Optimization: Contributed talks

Président de session: Renjie Chen

204 Condition Number Shrinkage by Joint Distributionally Robust Covariance-Precision Estimation

We propose a distributionally robust formulation for the simultaneous estimation of the covariance and precision matrix of a random vector. The proposed model minimizes the worst-case weighted sum of the Stein's loss of the precision matrix estimator and the Frobenius loss of the covariance estimator against all distributions from an ambiguity set centered at the empirical distribution. The radius of the ambiguity set is measured via convex spectral divergences. We show that the proposed distributionally robust estimation model reduces to convex optimization problems and thus gives rise to computationally tractable estimators. The estimators, as an outcome of distributional robustness, are shown to be nonlinear shrinkage estimators. The eigenvalues of the estimators are shrunk nonlinearly towards a scalar matrix, where the scalar is determined by the weight coefficient of the loss terms. We show that the shrinkage effect improves the condition number of the estimator. We provide the explicit expression of the shrinkage estimators induced by Kullback-Leibler divergence, Wasserstein divergence, Symmetrized Stein divergence, and Frobenius divergence. We also provide a parameter-tuning scheme that adjusts the shrinkage target and intensity that is asymptotically optimal. Numerical experiments on synthetic and real data show that our shrinkage estimators perform competitively against state-of-the-art estimators in practical applications.

Orateur: M. Renjie Chen (The Chinese University of Hong Kong)

ConditionNumber_slides_Paris.pdf

205 Solving Wasserstein Distributionaly Robust Optimization by regularization

Distributionaly robust optimization with Wassersein-distance uncertainty sets proves to be an outstanding tool to handle data heterogeneity and distribution shifts; see (Kuhn et al.)[2].
Recently, (Azizian et al.)[1] studied regularizations of WDRO problems. From a risk minimization problem $\min_{\theta\in\Theta}\mathbb{E}_\xi[\ell_\theta(\xi)]$ (ERM), it provides a dual formula (WDRO) for a robust estimator:
$$ \begin{align*} \min_{\theta\in\Theta;\lambda \geq 0} & \lambda \rho + \varepsilon ~ \frac1{N}\sum_{i=1}^N \left[ \log\left(\frac1{M}\sum_{j = 1}^M \left[ \exp{\left(\frac{\ell_\theta(\zeta_{ij}) - \lambda \|\xi_i - \zeta_{ij}\|^2}{\varepsilon }\right)}\right]\right) \right]\\ & \xi_i ~ \text{(N samples from the dataset)}\\ & \zeta_{ij} \sim \mathcal{N}(\xi_i, \sigma^2 I) ~ \text{(M "robustness" test points per sample).} \end{align*} $$ In this talk, we introduce $\texttt{SkWDRO}$ (Vincent et al.)[3], a python library that solves this problem efficiently, with multiple benefits: - it provides fine treatment of numerical aspects and choices of hyper-parameters - it offers a scikit-learn interface to solve some popular convex problems - it revolves around a PyTorch interface to reformulate a given $\ell_\theta$ loss module into its robust counterpart in only a few lines of code. [1]: Azizian Waïss, Iutzeler Franck and Malick, Jérôme: **Regularization for Wasserstein distributionally robust optimization**. *ESAIM COCV, 2023* [2]: Wiesemann Wolfram, Kuhn Daniel and Sim Melvyn: **Distributionally robust convex optimization**. *Operations research, INFORMS, 2014* [3]: Florian Vincent and Waïss Azizian and Franck Iutzeler and Jérôme Malick: **$\texttt{skwdro}$: a library for Wasserstein distributionally robust machine learning**. ArXiV, 2024

Orateur: Florian Vincent (Inria Grenoble, Laboratoire Jean Kuntzmann)

Florian_Vincent_ICSP_talk.pdf

206 A Note on Piecewise Affine Decision Rules for Robust, Stochastic, and Data-Driven Optimization

Multi-stage decision-making under uncertainty, where decisions are taken under sequentially revealing uncertain problem parameters, is often essential to faithfully model managerial problems. Given the significant computational challenges involved, these problems are typically solved approximately. This short note introduces an algorithmic framework that revisits a popular approximation scheme for multi-stage stochastic programs by Georghiou et al. (2015) and improves upon it to deliver superior policies in the stochastic setting, as well as extend its applicability to robust optimization and a contemporary Wasserstein-based data-driven setting. We demonstrate how the policies of our framework can be computed efficiently, and we present numerical experiments that highlight the benefits of our method.

Orateur: Simon Thomä (RWTH Aachen)

207 A Distributionally Robust Optimization Framework with Regularization Control

We propose a novel Wasserstein distributionally robust optimization (DRO) framework with regularization control that naturally leads to a family of regularized problems with user‐controllable penalization mechanisms. Our approach bridges the gap between conventional DRO formulations and practical decision-making by explicitly incorporating adverse scenario information into the optimization process, thereby enhancing robustness under unfavorable data conditions. In many stochastic programming applications, standard DRO methods based on Wasserstein distances could fail to capture decision-dependent perturbations or to adequately account for known out-of-sample adverse events. In contrast, our framework integrates adverse scenario information to yield solutions that remain resilient when conditions deteriorate. We provide rigorous finite-sample guarantees and show that, as the sample size increases, the corresponding regularization parameter scales appropriately so that both the optimal value and decision variables converge to those of the true stochastic program; in this way, the accumulation points of our solution sequence are optimal. Extensive numerical experiments on applications including the newsvendor problem and portfolio optimization illustrate that incorporating adverse scenarios into the regularization term can allow obtaining an advantageous balance between out-of-sample performance and robustness without sacrificing efficiency in stable environments.

Orateur: Diego Fonseca Valero (Universidad EAFIT)

Presentation_ICSP2025.pdf

Application in energy, finance or logistics: Contributed talks

Président de session: Peter Schütz (Norwegian University of Science and Technology)

208 Locating charging stations for battery-electric heavy-duty vehicles

We study the problem of locating charging stations for battery-electric heavy-duty vehicles (BEHDV) under uncertainty in both demand and available power grid capacity. The problem can be formulated as a two-stage stochastic problem where the first-stage decision is to determine the future locations of the charging stations. After the locations have been determined, information about demand and available power grid capacity is revealed and the second-stage decision is to install the chargers and satisfy demand.
The problem is formulated as a stochastic multi-period facility location problem with flow-based demand and a budget constraint. The objective of the model is to maximize expected demand coverage, i.e. maximizing the expected number of BEHDVs that can drive from their starting points to their destinations using the charging network. It does so within a set budget and while respecting limits on driving times and rest periods, available grid capacity, and spatial constraints for placing chargers. The model factors in vehicle types with varying battery capacities, as well as the route choices available to drivers. We use a multi-period approach to account for changes over time, such as variations in charging demand and fleet composition. We apply our model to a real-world case study based on a Norwegian operator of charging stations.

Orateur: Peter Schütz (Norwegian University of Science and Technology)

209 Stochastic Bilevel Waste-to-Energy pricing

Waste-to-energy (WtE) plants offer a way of treating waste while converting it to energy. This provides a more sustainable way of treating waste than common landfills. A vital part of a well-functioning waste management environment is the right price setting of gate fees, i.e., treatment price per amount of waste, for the WtE plants. The price setting can be described as a non-cooperative game where each player (WtE plant) tries setting its gate fee to maximize revenue. The amount of waste flowing to some plants depends on the gate fees of competition and the transportation costs from the waste producers (municipalities) to the given plant. Thus, the payoff function of each WtE plant forms a bilevel structure in which the leader (WtE plant) tries to maximize revenue while considering the follower’s reaction to the gate fee. All the municipalities that try to minimize their total waste processing costs cooperatively represent the follower. The best-response dynamics algorithm can find the Nash equilibrium of the considered game, but only when considering some limitations on feasible changes in gate fees. A more robust price setting, which can help to obtain a more realistic and stable outcome, can be provided if stochasticity is included in the problem. The most suitable parameter in the model that can be considered subject to stochastic influences is the amount of waste produced by the municipalities in the studied waste management network. Building on the heuristic proposed in the literature, the heuristic mathematical programs are enhanced to handle random variables. Each random variable corresponds to fluctuations of the waste production around the mean waste production of each municipality. After discussing possible reformulations of stochasticity in constraints and objective function, a corresponding deterministic equivalent to each stochastic program is presented. Then, the gate fees proposed by the novel stochastic-enhanced heuristics were tested against realizations solved by the original heuristics.

Orateur: Ivan Eryganov (Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology)

210 Optimizing multi-energy bids: a stochastic tri-level approach

In modern energy systems, electricity and natural gas markets are increasingly interdependent due to the prominent role of gas-fired power generation, which provides essential flexibility to balance the variability of renewable energy sources.
In such a context, this work presents a tri-level optimization model to address the optimal bidding problem faced by a price-maker electricity producer participating in both the day-ahead electricity and gas markets.
The producer, operating a diversified generation portfolio that includes gas-fired units, engages in both markets by purchasing natural gas as a fuel input and selling electricity across various generation technologies.
The upper level problem models the producer’s profit-maximization strategy, while the lower levels simulate the market clearing processes for gas and electricity, respectively.
Uncertainty in key parameters - such as demand, renewable generation, and competitor behavior - is captured through a stochastic formulation of the problem.
To address the computational complexity arising from the complexity and stochastic nature of the model, we employ neural network-based surrogate models to approximate market clearing outcomes.
Preliminary findings confirm the capability of the proposed model to capture complex intermarket dynamics and support more robust bidding strategies in multi-energy environments, while ensuring computational tractability through neural network-based approximations.

Orateur: Alessandra Rende (Department of Mechanical, Energy and Management Engineering, University of Calabria, Italy)

211 PTDF power flow for stochastic nodal capacity expansion planning with iterative scenario decomposition

Ensuring the reliability and resilience of the modern power grid requires models that handle the inherent uncertainty of generation availability and electricity consumption. These models must have sufficiently high spatial and temporal resolution to adequately capture weather variability and provide actionable siting and sizing decisions. A stochastic nodal capacity expansion planning (CEP) model can satisfy these requirements, but the presence of binary and integer variables in the optimization problem introduces challenges of computational scalability. We employ a power transfer distribution factors (PTDF) representation of power flow constraints within a stochastic nodal generation, transmission, and storage CEP model to reduce model size and improve solution time in an iterative approach. We implement a method to address the changes in system topology that occur during the optimization when this type of model is used. The method proposed consistently outperforms the more commonly used b-theta formulation of linear DC power flow in terms of the resulting optimal cost and computational solution time when applied to realistic test systems based on California and South Carolina.

Orateur: Tomas Valencia Zuluaga (Lawrence Livermore National Laboratory)

Contextual stochastic programming: Contributed talks

Président de session: Jonathan Li (Telfer School of Management, University of Ottawa)

212 Pessimistic bilevel optimization approach for decision-focused learning

The recent interest in contextual optimization problems, where randomness is associated with side information, has led to two primary strategies for formulation and solution. The first, estimate-then-optimize, separates the estimation of the problem's parameters from the optimization process. The second, decision-focused optimization, integrates the optimization problem's structure directly into the prediction procedure. In this work, we propose a pessimistic bilevel approach for solving general decision-focused formulations of combinatorial optimization problems. Our method solves an $\varepsilon$-approximation of the pessimistic bilevel problem using a specialized cut generation algorithm. We benchmark its performance on the 0-1 knapsack problem against estimate-then-optimize and decision-focused methods, including the popular SPO+ approach. Computational experiments highlight the proposed method's advantages, particularly in reducing out-of-sample regret.

Orateur: Diego Jiménez (SKEMA Business School - KU Leuven)

213 Conditional Risk Minimization with Side Information

We present a unified framework and practical solution for conditional risk minimization with side information—interpretable, tractable, and backed by finite-sample statistical guarantees.

Orateur: Prof. Jonathan Yu-Meng Li (Telfer School of Management, University of Ottawa)

214 Integrated learning and stochastic optimization for the design of distribution networks under endogenous uncertainty

This work addresses the design and planning of a two-echelon omnichannel distribution network under endogenous uncertainty. The network consists of suppliers, retail stores, and distribution centers (DC) that serve a dual role i.e., replenishing retail stores and fulfilling direct-to-customer deliveries. We focus on strategic decisions such as the opening and configuration of distribution centers and the allocation of transportation capacity across the network. These decisions are supported by operational decisions related to inventory deployment and replenishment, as well as the assignment of customer orders to fulfillment channels. We formulate a multi-period two-stage stochastic program that maximizes the expected profit while balancing DC deployment costs, operational costs, and service responsiveness. In the first stage, the strategic design decisions are made before demand realization. In the second stage, after demand is revealed, we tackle operational decisions – inventory replenishment and the assignment of customer orders to fulfillment channels. Since the customers' willingness to order online depends on the Order-To-Delivery (OTD) time offered by the retailer, through the location of its DCs, this adds an endogenous uncertainty to the model. We integrate machine learning with stochastic optimization to tackle the model through an iterative learning-and-optimization approach. We predict demand in each iteration based on the current network configuration, reflecting factors such as service offers, OTD time, inventory availability, and responsiveness. These predictions are used to generate demand scenarios over operational periods, which inform the resolution of the two-stage stochastic program. The process repeats until convergence, that is, when the optimized network configuration becomes consistent with the structure used to generate demand scenarios.

Orateur: Linda Ben Ismail

ML: Contributed talks

Président de session: Dr Philip Thompson (FGV-EMAp)

215 On stochastic mirror descent under relative nonconvexity

The notions of relative (weak) convexity and variation (e.g., Lipschitzness and smoothness) have been successfully applied to some optimization problems, including applications in machine learning. While typically harder to prove, these properties encode better dependence of the objective with respect to the intrinsic geometry of the problem. We review previous analysis of the mirror descent method under relative properties and present novel convergence analysis within this framework. In particular, we consider relative notions of the Polyak-Łojasiewicz inequality and its consequences. If time permits, we will also present some applications in machine learning.

Orateur: Dr Philip Thompson (FGV-EMAp)

216 Linear Convergence Rate in Convex Setup is Possible! First- and Zero-Order Algorithms under Generalized Smoothness

The gradient descent (GD) method -- is a fundamental and likely the most popular optimization algorithm in machine learning (ML), with a history traced back to a paper in 1847 (Cauchy, 1847). In this paper, we provide an improved convergence analysis of gradient descent and its variants, assuming generalized smoothness (L0,L1). In particular, we show that GD has the following behavior of convergence in the convex setup: At first, the algorithm has linear convergence, and approaching the solution, has standard sublinear rate. Moreover, we show that this behavior of convergence is also common for its variants using different types of oracle: Normalized Gradient Descent as well as Clipped Gradient Descent (the case when the oracle has access to the full gradient); Random Coordinate Descent (when the oracle has access only to the gradient component); Random Coordinate Descent with Order Oracle (when the oracle has access only to the comparison value of the objective function). In addition, we also analyze the behavior of convergence rate of GD algorithm in a strongly convex setup.

Orateur: Aleksandr Lobanov (MIPT)

Sequential decision-making under uncertainty: New developments in Stochastic Dual Dynamic Programming

Président de session: Bernardo Freitas Paulo da Costa (Fundação Getulio Vargas)

217 Stochastic dual dynamic programming for log-linear autoregressive uncertainty in the right-hand side

We consider the generation of cuts in stochastic dual dynamic programming (SDDP) for multistage stochastic linear programming problems with stagewise dependent uncertainty in the right-hand side described by log-linear (or geometric) autoregressive processes. We show that it is possible to develop tractable closed-form cut formulas in this case. The cuts are linear in all decision variables, and thus can be directly incorporated into the subproblems in SDDP without compromising their linearity. If solvers do not allow for this, our formulas can be used to adapt the intercept of a given cut to a scenario at hand in a computationally tractable way. Our findings are supported by an extensive computational study of a hydrothermal scheduling problem.

Orateur: Dr Christian Füllner (Karlsruhe Institute of Technology)

218 Multicyclic multistage stochastic programming using daisy chains in the electricity market

Hydropower scheduling is an important application of stochastic dynamic programming, involving large optimization problems with intertemporal dependency and complex dynamics. The nature of this problem is naturally seasonal (and therefore cyclic), and even though most real-world use cases usually apply discretization strategies (such as monthly, weekly or daily time steps) it is reasonable to expect that these are approximations of an underlying continuous time representation. Different discretization strategies are explored in this paper using functionalities of IARA (https://iara.psr-inc.com/), a novel open-source tool for Interaction Assessment between Regulators and Agents.

Orateur: M. Gabriel Vidigal (PSR)

219 Stopping SDDP using sequential testing

We develop a new stopping rule for the stochastic dual dynamic programming (SDDP) algorithm based on sequential testing. Traditional stopping rules are based on statistical tests that assess whether the optimality gap in a given iteration is smaller than a pre-defined precision. However, repeated use of such single-iteration tests invalidates the overall validity of the stopping rule, because the probabilities of false positives (i.e., stopping too early) of the individual tests compound. To overcome this problem, we use ideas from sequential hypothesis testing to construct a statistically valid stopping rule. This stopping rule is based on a hypothesis test that uses joint information from multiple iterations of the algorithm. Besides ensuring statistical validity, another benefit of this approach is that it can exploit the fact that "weak evidence" for convergence in several subsequent iterations amounts to strong overall evidence for convergence.

Orateur: Ruben van Beesten (Erasmus University Rotterdam)

220 Relative Value Iteration for Infinite-Horizon SDDP: Application to Hydroelectric Problem

This work addresses the challenges of applying Stochastic Dual Dynamic Programming (SDDP) to infinite-horizon hydroelectric water management problems with continuous state and control spaces. While SDDP has proven effective in finite-horizon settings, its extension to the infinite-horizon case with a discount factor close to one introduces numerical difficulties when the discount rate is close to 1. To improve convergence, we propose a modified SDDP algorithm inspired by relative value iteration, incorporating additive shifts to accelerate the relevance of generated cuts. Numerical experiments highlight the practical benefits of our approach for long-term planning.

Orateur: Francis Durand (Université Sorbonne Paris Nord)

Stochastic integer programming: Advancement in Stochastic Discrete Optimization

Président de session: Haoxiang Yang

221 Efficient Cutting-Plane Methods for Multistage Stochastic Mixed-Integer Programming

Multistage stochastic mixed-integer programming (MS-MIP) is a powerful framework for sequential decision-making under uncertainty, yet its computational complexity poses significant challenges. This paper presents a convergent cutting-plane algorithm for solving MS-MIP with binary state variables. Our method exploits a geometric interpretation of the convex envelope of value functions and the convex hull of feasible regions. By employing the cutting-plane tree algorithm, we iteratively refine LP relaxations using multi-term disjunctive cuts (MDCs) and generate Benders’ cut to construct precise approximations of the value functions, eliminating the need for solving MIP subproblems to generate tight cuts. A key theoretical contribution of this work is proving the finite convergence of our proposed algorithm. Through a toy example, we provide a clear illustration to demonstrate how MDCs strengthen LP relaxation. However, we also highlight the drawbacks of MDCs, such as their adverse impact on overall computational performance due to the increased problem size and complexity. To address this issue, we propose an improved strategy that balances the trade-off between cut strength and computational efficiency, ensuring the practical applicability of the approach. Computational experiments on generation expansion planning validate its efficiency and scalability in solving large-scale MS-MIP problems.

Orateur: Hanbin Yang (The Chinese University of Hong Kong, Shenzhen)

222 Bundle-ADMM: A Robust and Efficient Decomposition Method for Large-Scale Mixed-Integer Programs

Large-scale mixed-integer programs (MIPs) pose significant computational challenges due to their complexity, nonconvexity, and nonsmooth dual functions. Traditional decomposition methods often suffer from slow convergence, sensitivity to parameters, and instability. We propose Bundle-ADMM, a novel method combining the Alternating Direction Method of Multipliers (ADMM) and bundle techniques to stabilize dual updates and accelerate convergence. Computational results on electric grid planning problems demonstrate that Bundle-ADMM significantly improves stability and convergence efficiency compared to conventional approaches.

Orateur: Kibaek Kim (Argonne National Laboratory)

223 Global Optimization of Pandemic Staged Alert Systems via Bayesian Optimization

Staged alert systems have been successfully implemented to minimize socioeconomic losses while avoiding overwhelming healthcare systems. Optimizing such systems can be formulated as a challenging two-stage stochastic mixed-integer programming problem with a discontinuous recourse function, where decision variables reside in a discrete space. Traditional simulation-based optimization techniques often assume continuity and smoothness in objective functions, while metaheuristics lack optimality guarantees. We propose a novel approach combining Gaussian process-based Bayesian optimization with a methodology tailored to handle discontinuities and efficiently navigate discrete search spaces. We establish ​global optimality guarantees with convergence properties. The efficacy of our method is demonstrated by optimizing stage thresholds in a pandemic alert system, providing a principled framework for discrete stochastic optimization under discontinuity.

Orateur: Zhuo Zhang

Mini-symposium: Multihorizon Stochastic Programming: Models, Algorithms, and Applications

Président de session: Harsha Gangammanavar (Southern Methodist University)

224 Models and algorithms for multihorizon stochastic programming

This presentation addresses stochastic optimization models for the energy transition, focusing on multiscale multihorizon systems. We model both long-term investment decisions—such as renewable generation, carbon capture, and decarbonized transport—and short-term operations like storage management and system balancing. To handle uncertainty across both scales, we introduce multihorizon stochastic programming, a framework that captures uncertainty in both strategic and operational time steps. The model structure enables decomposition methods, and we present computational results showing how uncertainty at multiple scales critically shapes optimal energy transition strategies.

Orateur: Prof. Asgeir Tomasgard (NTNU)

225 Handling of long-term storage in multi-horizon stochastic programs

We show how to implement long-term storage in the multi-horizon modelling paradigm, expanding the range of problems this approach is applicable to. The presented implementation is based on the HyOpt optimization model, but the ideas are generic.
We illustrate the effects of several formulations on a simple case of electrification of an offshore installation using wind turbines and a hydrogen-based energy-storage system. The results show that the formulations provide reasonable modelling of the storage capacity, without sacrificing the advantages of the multi-horizon approach.

Orateur: Michal Kaut (SINTEF)

multi-horizon_storage.pdf

related paper

226 Multi-horizon optimization for domestic renewable energy system design under uncertainty

In this talk we address the challenge of designing optimal domestic renewable energy systems under multiple sources of uncertainty appearing at different time scales. Long-term uncertainties, such as investment and maintenance costs of different technologies, are combined with short-term uncertainties, including solar radiation, electricity prices, and uncontrolled load variations.
We formulate the problem as a multistage multi-horizon stochastic Mixed Integer Linear Programming (MILP) model, minimizing the total cost of a domestic building complex’s energy system. The model integrates long-term investment decisions, such as the capacity of photovoltaic panels and battery energy storage systems, with short-term operational decisions, including energy dispatch, grid exchanges, and load supply. To ensure robust operation under extreme scenarios, first- and second-order stochastic dominance risk-averse measures are considered preserving the time consistency of the solution.
Given the computational complexity of solving the stochastic MILP for large instances, a rolling horizon-based matheuristic algorithm is developed. Additionally, various lower-bound strategies are explored, including wait-and-see schemes, expected value approximations, multistage grouping and clustering schemes. Extensive computational experiments validate the effectiveness of the proposed methods on a case study based on a building complex in South Germany, tackling models with over 20 million constraints, 5 million binary variables, and 6 million continuous variables.

Orateur: Giovanni Micheli (University of Bergamo)

227 The impact of wind uncertainty modelling on power systems investment planning under multi-timescale uncertainty

This paper proposes a novel algorithm to efficiently solve large-scale multi-stage stochastic programs with block separable recourse. We use an extended Benders decomposition with adaptive oracles to decompose the problem into a master problem and a collection of subproblems. The adaptive oracles enable cut sharing among the subproblems. We apply the proposed method for solving power system capacity expansion planning problems with multi-timescale uncertainty. The problem is formulated as a multi-horizon stochastic program, which fits the problem structure we deal with. We consider long-term uncertainty in power demand scaling and short-term uncertainty in wind capacity factor. We present and analyse the results of different ways of modelling short-term wind uncertainty.

Orateur: Dr Hongyu Zhang (University of Southampton)

Mini-symposium: Structured learning and stochastic combinatorial optimization: methodological perspectives and applications

Président de session: Axel Parmentier (CERMICS, École Nationale des Ponts et Chaussées)

228 Combinatorial Optimization-Agmented Machine Learning

In this talk, we will bridge the gap between combinatorial optimization and machine learning to derive policies for contextual multi-stage decision-making problems that arise in various stochastic settings, including transportation, control, and supply chain management. We will discuss how to encode effective policies by embedding combinatorial optimization layers into neural networks and training them with decision-aware learning techniques. Specifically, I will provide an overview of the underlying algorithmic pipelines and foundations, and elucidate two paradigms - learning by experience and learning by imitation - to train the pipeline’s statistical models in an end-to-end fashion. I will demonstrate the efficacy of optimization-augmented machine learning pipelines for selected application cases, among others discussing its winning performance on the 2022 EUROMeetsNeurIPS dynamic vehicle routing challenge. Finally, we will put the presented paradigms into perspective and learn how they can also be used to approximate (static) equilibrium problems, focusing on traffic equilibria as a use case.

Orateur: Dr Maximilian Schiffer (TUM)

229 Joint Learning of Energy-based Models and their Partition Function

Orateur: Dr Mathieu Blondel (Google)

230 Primal-dual algorithm for contextual stochastic combinatorial optimization

As industry seeks to make its processes more resilient, data driven optimization is gaining momentum in Operation Research. Resilience involves managing uncertainty when optimizing supply chains, while efficiency requires scalable combinatorial optimization algorithms, as most gains from operations research algorithms come from decreasing marginal costs. This underscores the need for scalable algorithms for combinatorial and stochastic optimization problems, whether they are dynamic, tactical, or strategic. Policies encoded as neural networks with a combinatorial optimization layer have demonstrated their efficiency in these settings when trained in a decision-focused manner. Until now, such policies have been trained using supervised learning, often based on Fenchel-Young losses, and considered as heuristics. We instead focus on risk minimization. By leveraging the connection between Fenchel-Young losses and Bregman divergences, we introduce a deep learning-compatible primal-dual algorithm and show that it converges to the optimum of the empirical risk minimization problem in some settings. This new approach has two advantages. First, numerical experiments show that it learns better policies. Second, we prove some generalization properties that provide upper bounds on the optimality gap, which hold in expectation.

Orateur: Axel Parmentier (CERMICS, École Nationale des Ponts et Chaussées)

12:45 Lunch

Application in energy, finance or logistics: Contributed talks

Président de session: Vittorio Moriggia (Université de Bergame)

231 Goal-based investments with target priorities

A Dynamic Stochastic Programming model applied to long-term Asset and Liability Management portfolio selection faces the challenge to satisfy an investor’s personal goals. Since not all the targets have the same priority, we ask the model to take the investor’s expectations into account.
These kinds of problems are of particular interest to the insurance industry, where they are commonly applied to pension fund customers with time horizons that can span decades.
The model addresses uncertainty in asset returns and liabilities through a stochastic scenario generation process for key financial variables, as detailed in [1]. The objective function is designed to optimize the risk-return tradeoff, incorporating investor-specific targets and constraints within a multi-period stochastic programming framework, as proposed in [2].
The proposed novelty here is the possibility to adapt the desired goals to the personal preferences of the investor.
Our proposal lies in the model's ability to dynamically adapt investment goals to the investor’s individual preferences and priorities, providing a personalized and flexible approach to long-term portfolio planning.
References
[1] M. Kopa, V. Moriggia, and S. Vitali. Individual optimal pension allocation under stochastic dominance constraints. Annals of Operations Research, 260(1-2):255–
291, 2018.
[2] G. Consigli, V. Moriggia, and S. Vitali. Long-term individual financial planning under
stochastic dominance constraints. Annals of Operations Research, 292(2):973–1000,
2020.

Orateur: Vittorio Moriggia (Université de Bergame)

232 Optimal hedging of the interest rate swap book

Interest rates on financial markets are noisy. This is reduced by a Kalman filter, which gives better measurement of interest rate cuts and hikes. With an optimization model interest rate curves are measured with increased accuracy from Overnight Index Swaps. Principal Component Analysis identifies the significant risk factors in interest rate markets. With these a Stochastic Programming model is formulated to determine the optimal hedge of the Overnight Index Swap book, where significant improvements are found relative to traditional delta hedging.

Orateur: Jörgen Blomvall (Linköping university)

233 INCORPORATION OF RISK METRICS IN ELECTRIC SYSTEM EXPANSION PLANNING AND PORTFOLIO EFFICIENCY ANALYSIS

This work presents a methodology for incorporating risk measures into the energy system expansion planning process. The approach involves a decomposed investment and operation model, where the objective function is modified to progressively place greater emphasis on minimizing the risk metric. By doing so, it is possible to calculate risk levels for different optimal expansion plans. The concept of the efficient frontier, borrowed from Modern Portfolio Theory (Markowitz), is applied to evaluate trade-offs between total costs and associated risks across various expansion plans. It provides a more robust framework for decision-making in long-term planning, balancing cost-effectiveness with risk mitigation strategies. The derivation of different optimal plans, each associated with a calculated risk, enables the construction of the efficient frontier curve, which offers a visual representation of the trade-offs between cost and risk for various expansion portfolios.

Orateur: Lucas Guerreiro (PSR)

Application in energy, finance or logistics: Contributed talks

Président de session: Guzin Bayraksan (The Ohio State University)

234 A Data-Driven Robust Optimization Approach for the Strategic Operation and Sizing of a Thermal–PV–Storage Hybrid Power Plant in Multi-Timescale Electricity Markets

We study a robust optimization framework for the optimal operation and sizing of a hybrid virtual power plant (VPP) composed of a thermal generator unit (TGU), a large-scale photovoltaic (PV) plant, and an energy storage system (ESS). The VPP participates as a price-taker in both the day-ahead (DA) and real-time (RT) electricity markets, offering energy and ancillary services (i.e., frequency regulation) across multiple timescales.

The energy management strategy is formulated as a self-scheduling unit commitment (UC) problem over extended horizons, allowing long-term energy sales estimation and enabling sizing of the hybrid plant components (PV and BESS). The TGU is modeled using a network flow formulation, enhanced with problem-specific cutting planes to strengthen it and reduce the overall solution time for corresponding mixed-integer problems.

A data-driven, robust optimization approach addresses uncertainty in solar production and market prices. Polyhedral uncertainty sets are constructed from historical data to capture temporal patterns and variability, ensuring resilient and reliable operation under uncertain future conditions. In the short term, the proposed model determines energy bids in the DA market with hourly granularity and adjusts offers in the RT market with finer temporal resolution while considering the physical constraints of all plant components.

Numerical results based on one year of historical data demonstrate the effectiveness of the proposed approach in maximizing long-term profits and enabling robust sizing and operation of the hybrid power plant under uncertainty.

Orateur: José Ignacio Delgado Anguita (Universidad Técnica Federico Santa María)

235 Operating a battery at minimum cost for reserve commitment using energy arbitrage

Consider an electric battery whose owner has committed with a transmission system operator (e.g., RTE in France) to making at its disposal a "reserve'" of electricity along a given day: every hour, a random quantity will be discharged from or charged to the battery; the commitment is on the range of this random variable. To respond at best to this commitment, the owner of the battery can buy or sell electricity every hour on the "intraday" market, at prices following a random process. Moreover, there is a maximal energy level, a bound on the maximal variation of this level, and an extra final cost anticipating the future; the exact value of both the reserve activation and the price is only revealed at the last moment. The problem consists in finding a policy minimizing the expected cost of ensuring satisfaction of the commitment. To the authors' knowledge, this problem has not been addressed yet.

Orateur: Rose Sossou Edou (École nationale des ponts et chaussées)

236 Prescriptive Energy Scheduling in Two-Stage Markets: an Iterative Learning Approach

Energy scheduling is typically conducted as a two-stage procedure that comprises day-ahead and real-time stages. Particularly, day-ahead decisions are made under uncertainty, which then affects real-time decisions, as operators must constantly maintain power balance. For that, it is commonplace in the energy industry to predict renewable energy production and power load, which are then used to plan energy dispatch ahead of time. However, forecasting models are often developed independently of the sequential decision-making process, which can result in sub-optimal day-ahead solutions. While scheduling methods based on stochastic programming have been developed to incorporate the influence of day-ahead decisions on real-time decision problems across different scenarios, they have been criticized for undermining key market characteristics and the computational burden during operations. To bridge the gap, we design a value-oriented point forecasting approach for sequential energy dispatch problems with renewable energy sources. During the training phase, we align the training objectives with the decision value, aiming to minimize total operational costs. The estimation of forecasting model parameters is set up as a bilevel programming problem. With certain mild assumptions, we reformulate the upper-level objective into an equivalent form utilizing the dual solutions from the lower-level operation problems. In particular, we design a novel iterative learning method tailored for the defined bilevel program. Within this iterative framework, we demonstrate that the upper-level objective is locally linear regarding the forecasting model's output, which then serves as the loss function. Through numerical experiments, it is shown that the proposed method provides reduced operating costs compared to the widely utilized sequential decision-making scheduling framework. Simultaneously, the method attains a performance level akin to two-stage stochastic programs, while offering greater computational efficiency.

Orateur: Honglin Wen (Shanghai Jiao Tong University)

ML: Neural networks with combinatorial optimization layers: encoding policies for (multistage) stochastic combinatorial optimization

Président de session: Léo Baty (Ecole des Ponts)

237 Structured Reinforcement Learning

When facing contextual multi-stage optimization problems, training combinatorial optimization-enriched machine learning pipelines (ML-CO-pipelines) to date either requires imitating expert solutions or utilizing unstructured learning algorithms. While the former restricts the use of ML-CO-pipelines to problems with traceable offline solutions and relatively homogenous state spaces, the latter fails to account for combinatorial action spaces, which can destabilize training.
To mitigate the respective drawbacks, we introduce structured reinforcement learning (SRL), enabling the stable training of ML-CO pipelines using only collected experience. In the core of its training process, SRL generates and evaluates several actions by perturbing the ML model’s output and subsequently performs an update step towards the best actions using a Fenchel-Young loss.
We test SRL in three static and three dynamic environments, representing various industrial applications. We find SRL to substantially outperform structured imitation learning and unstructured RL, attributing to its enhanced exploration of the combinatorial state-action space and to its improved training stability.

Orateur: Heiko Hoppe (Technical University of Munich)

ICSP_Presentation_Heiko_Hoppe.pdf

238 Primal-dual algorithm for multistage stochastic optimization

Multistage stochastic optimization (MSO) is pivotal for sequential decision-making under uncertainty, with prominent approaches in stochastic optimal control and reinforcement learning. While methods like Stochastic Dual Dynamic Programming excel with moderate-dimensional states and large continuous control spaces, and reinforcement learning handles large state spaces with smaller control sets, a significant gap exists for dynamic operations research problems. These problems are characterized by high-dimensional state spaces and discrete, combinatorially large control spaces.

Policies based on Combinatorial Optimization Augmented Machine Learning (COAML) have recently demonstrated success in tackling such complex problems, notably in dynamic vehicle routing. However, current state-of-the-art learning algorithms for these policies typically rely on imitating anticipative decisions. This often translates to supervised learning problems using Fenchel-Young losses, which can result in "voting" type policies that underperform on problems requiring strong temporal coordination between decisions.

To address this limitation and foster better coordination, we introduce multistage extensions of Fenchel-Young losses. These novel loss functions are integrated into an empirical cost minimization algorithm. Preliminary numerical results on benchmark environments indicate that our approach significantly improves upon existing methods by enabling more coordinated decision-making in multistage stochastic settings.

Orateur: Solène Delannoy-Pavy (CERMICS / RTE)

239 Combinatorial optimization and decision-focused learning for stochastic tail assignment

Network schedule optimization is one of the main applications of OR to the air transport industry. This process involves designing aircraft schedules that are both operationally feasible and cost-optimal. Tail assignment is the process of assigning specific aircraft (tails) to planned flights, typically occurring a few days to weeks before operations. Airlines routinely solve this problem using Mixed Integer Linear Programming (MILP). However, these methods often overlook the resilience of routing solutions to delays and the associated costs of delay propagation along planned routes. While airlines commonly mitigate delay impacts by adding artificial time buffers between flights as hard constraints, this approach is frequently suboptimal and can lead to infeasible instances in practice, limiting its operational utility.

We propose a novel approach to the tail assignment problem that explicitly accounts for delay propagation in flight schedules. Our method consists of two key components. First, we develop a neural network-based delay prediction and propagation model trained on historical data, which we use to generate realistic delay scenarios and evaluate the delay costs of candidate tail assignments. Second, we implement a decision-focused learning approach that encodes an assignment policy as a deep learning pipeline combined with the tail assignment MILP as a combinatorial optimization layer. This policy is trained in a supervised manner using high-quality solutions computed offline via column generation.

Experimental results demonstrate that our approach generates tail assignment solutions that significantly reduce the total cost (operational + delay costs) compared to traditional methods, while maintaining computational efficiency comparable to deterministic tail assignment algorithms. This makes our solution practical for real-world airline operations, where both solution quality and quick decision-making are essential.

Orateur: Léo Baty (Ecole des Ponts)

ML: Stochastic gradient methods for reinforcement learning and optimal control

Président de session: Caleb Ju (Georgia Tech)

240 A General-Purpose Theorem for High-Probability Bounds of Stochastic Approximation with Polyak Averaging

Polyak averaging is a well-known technique for achieving asymptotically optimal convergence in Stochastic Approximation. In this work, we establish the first high-probability bound for general Stochastic Approximation with Polyak Averaging. We take a black-box approach, assuming access to an anytime high-probability bound for a given Stochastic Approximation, and derive tight finite-time bounds for its Polyak-averaged version. Applying our black-box framework to general contractive Stochastic Approximation, we analyze the impact of averaging under various settings.

Orateur: Sajad Khodadadian (Virginia Tech)

241 Safe-EF: Error Feedback with Applications to Distributed Safe Reinforcement Learning

Federated learning faces severe communication bottlenecks due to the high dimensionality of model updates. Communication compression with contractive compressors (e.g., Top-K) is often preferable in practice but can degrade performance without proper handling. Error feedback (EF) mitigates such issues but has been largely restricted to smooth, unconstrained problems, limiting its real-world applicability where non-smooth objectives and safety constraints are critical. We advance our understanding of EF in the canonical non-smooth convex setting by establishing new lower complexity bounds for first-order algorithms with contractive compression. Next, we propose Safe-EF, a novel algorithm that matches our lower bound (up to a constant) while enforcing safety constraints essential for practical applications. Extending our approach to the stochastic setting, we bridge the gap between theory and practical implementation. Extensive experiments in a reinforcement learning setup, simulating distributed humanoid robot training, validate the effectiveness of Safe-EF in ensuring safety and reducing communication complexity.

Orateur: Ilyas Fatkhullin (ETH Zürich)

242 Strongly-polynomial time and validation analysis of policy gradient methods

We propose a novel termination criterion, termed the advantage gap function, for finite state and action Markov decision processes (MDP) and reinforcement learning (RL). By incorporating this advantage gap function into the design of step size rules and deriving a new linear rate of convergence that is independent of the stationary state distribution of the optimal policy, we demonstrate that policy gradient methods can solve MDPs in strongly-polynomial time. To the best of our knowledge, this is the first time that such strong convergence properties have been established for policy gradient methods. Moreover, in the stochastic setting, where only stochastic estimates of policy gradients are available, we show that the advantage gap function provides close approximations of the optimality gap for each individual state and exhibits a sublinear rate of convergence at every state. The advantage gap function can be easily estimated in the stochastic case, and when coupled with easily computable upper bounds on policy values, they provide a convenient way to validate the solutions generated by policy gradient methods. Therefore, our developments offer a principled and computable measure of optimality for RL, whereas current practice tends to rely on algorithm-to-algorithm or baselines comparisons with no certificate of optimality.

Orateur: Caleb Ju (Georgia Tech)

Stochastic integer programming: Contributed talks

Président de session: Ricardo Fukasawa (University of Waterloo)

243 A Two-Step Warm Start Method Used for Solving Large-Scale Stochastic Mixed-Integer Problems

Solving large-scale stochastic optimization problems is challenging, especially when uncertainties are represented by a large number of scenarios. To tackle this, we introduce TULIP ("Two-step warm start method Used for solving Large-scale stochastic mixed-Integer Problems"), an efficient approach for solving two-stage stochastic (mixed) integer programs with an exponential number of constraints. TULIP consists of two steps: we first generate a reduced set of representative scenarios and solve the root node of the corresponding integer linear program using a cutting-plane method. The generated constraints are then used to accelerate solving the original problem with the full scenario set in the second phase. We demonstrate the generic effectiveness of this method on two benchmark problems: the Stochastic Capacitated Vehicle Routing Problem and the Two-Stage Stochastic Steiner Forest Problem. In our numerical experiments, we find that TULIP yields significant computational gains compared to solving the problem directly with branch-and-cut.

Orateur: Berend Markhorst (CWI)

244 Approximating Value Functions via Corner Benders’ Cuts

We introduce a novel technique that generates Benders cuts from a corner relaxation of the target higher-dimensional polyhedron. Moreover, we develop a computationally efficient method to separate facet-defining inequalities for the epigraph
associated with this corner relaxation. By leveraging a known connection between arc-flow and path-flow formulations, we show that our method can recover the linear programming bound of a Dantzig-Wolfe formulation using multiple cuts in the projected space. We validate our approach with computational experiments on the vehicle routing problem with stochastic demands (VRPSD), a well-studied variant of the classic capacitated vehicle routing problem (CVRP) that accounts for customer
demand uncertainty. Computational experiments show that our generic technique can enhance the performance of a problem-specific state-of-the-art algorithm for the VRPSD.

Orateur: Ricardo Fukasawa (University of Waterloo)

245 A Finitely Converging Price-And-Cut Framework for Two-Stage Stochastic Programming

We present a general price-and-cut procedure for two-stage stochastic integer programs with complete recourse, and first-stage binary variables. We propose a novel set of cutting planes that can close the optimality gap when added to the Dantzig-Wolfe decomposition master problem. It is shown to provide a finite exact algorithm for a number of stochastic integer programs, even in the
presence of integer variables or continuous random variables in the second stage. Moreover, we propose stabilization techniques to reduce computation time. We apply the methodology to an application in energy. In this problem, the goal is to improve the resilience of the electricity grid using mobile power generators in the aftermath of a natural disaster. In the first stage of the problem, we decide which substations in the network to adapt to allow mobile power generators to connect to the grid, whereas the second-stage decisions are how to employ the mobile power generators.

Orateur: Laurens Elderhorst (University of Groningen)