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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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,...
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...
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...
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...
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...
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....
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...
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...
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...
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...
- 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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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.
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...
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...
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...
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...
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...
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...
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...
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...
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.
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...
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,...
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...
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...
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...
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,...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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.
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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.
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...
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...
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...
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...
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...
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...
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...
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...
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...
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)....
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,...
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.
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...
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...
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...
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...
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...
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...
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...
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 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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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....
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...
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...
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...
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...
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...
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...
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...
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...
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...
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,...
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...
We present a unified framework and practical solution for conditional risk minimization with side information—interpretable, tractable, and backed by finite-sample statistical guarantees.
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...
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...
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)...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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)...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
Tri-level defender-attacker game models are a well-studied method for
determining how best to protect a system (e.g., a transportation network) from attacks.
Existing models assume that defender and attacker actions have a perfect effect, i.e.,
system components hardened by a defender cannot be destroyed by the attacker, and
attacked components always fail. Because of these assumptions,...
Climate variability is increasingly affecting energy generation, particularly renewable sources that depend directly on weather patterns. Variations in temperature, precipitation, and wind patterns are altering the availability and reliability of hydropower, wind, and solar energy, posing challenges for power system stability and long-term planning. As climate patterns shift, our perception of...
We discuss a new electric car ferry operating along the west coast of Norway. The ferry visits a total of 17 different ports, of which only three are mandatory stops. It can carry up to 27 standard cars across three lanes. Depending on the loading arrangement, cars may need to reverse onto or off the ferry. In some cases, vehicles may also need to disembark at an intermediate port and reboard...
It is often the case where historical data used to represent uncertainty need some expert-based opinion before being suitable for use in a planning problem. For instance, in a renewable energy and energy storage planning (REESP) problem, the solar generation data may be gathered using older generation of solar panel technology while the nowel solar panels intended for planning have improved...
Optimization under uncertainty often relies on sampling the uncertainty to evaluate some expectations or to work with probability constraints. As the dimension of the random variable grows, the applicability of this approach diminishes, as achieving non-trivial precision through sampling may require too many samples to be practical.
We propose an alternative approach, where the probability...
We study the design of large-scale relay logistics hub networks that are resilient to demand variability. We formulate a two-stage stochastic optimization model that integrates first-stage strategic decisions on hub location and capacity with second-stage tactical decisions on consolidation-based routing. To solve this problem exactly, we develop a three-stage branch-and-cut algorithm with...
We study a multidimensional mechanism design problem where a seller offers multiple products to a single buyer. The seller possesses only marginal distributional information about the buyer's random valuation of each product. The buyer is not a perfect optimizer and is satisficing whenever his incentive is epsilon away from the optimal---a notion called approximate incentive compatibility...
Federated learning enables training machine learning models while preserving the privacy of participants. Surprisingly, there is no differentially private distributed method for smooth, non-convex optimization problems. The reason is that standard privacy techniques require bounding the participants' contributions, usually enforced via clipping of the updates. Existing literature typically...
