Présidents de session
Stochastic Programming: Contributed talks
- Daniel Mimouni (Mines Paris / IFPEN)
Stochastic Programming: Computational Methods For Stochastic Optimization
- Robert Bassett (Naval Postgraduate School)
Stochastic Programming: Applications of Stochastic Programming in Statistics and Risk Management
- Johannes Royset (University of Southern California)
- Anton Malandii (Stony Brook University)
Stochastic Programming: Contributed talks
- Anton Kleywegt (Georgia Institute of Technology)
Stochastic Programming: Stochastic Optimization in Infinite-Dimensional Spaces
- Patrick Combettes (North Carolina State University)
Stochastic Programming: Contributed Talks
- Il n'a pas de président de session pour ce bloc
Stochastic Programming
- Bernardo Freitas Paulo da Costa (Fundação Getulio Vargas)
Stochastic Programming: Contributed talks
- Claudia Sagastizábal
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...
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...
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 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...
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...
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...
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...
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...
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...
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...
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 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...
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...
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...
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,...
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...
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 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 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.
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...
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...
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...
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...
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...
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...
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...
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...
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...
Two-stage stochastic programs with finite support are a fundamental tool for decision-making under uncertainty. However, their computational tractability is often limited by the number of scenarios considered. To address this issue, scenario clustering methods have been proposed to reduce the problem size while preserving the essential characteristics of the uncertain parameters that drive the...
We investigate the elicitation method for the Von Neumann–Morgenstern-type decision-maker (DM) from pairwise comparison data in the presence of response errors. We apply the maximum likelihood estimation (MLE) method to elicit the nominal utility, together with the variance of the response error, assuming a Gumbel distribution. Given the finite support of the pairwise comparison lotteries and...
