Risk measures incorporate a conservative or risk averse perspective in decisionmaking under uncertainty. Taking a variety of models for the potential outcomes into account, the distributionally robust decision is the most conservative decision among the decisions available. This paper investigates different versions of conditional risk measures and distributionally robust functionals in a multistage setting. The … Read more
The aim of this paper is to formulate several questions related to distributionally robust Stochastic Optimal Control modeling. As an example, the distributionally robust counterpart of the classical inventory model is discussed in details. Finite and infinite horizon stationary settings are considered. ArticleDownload View PDF
In this paper, we discuss Optimal Control and Markov Decision Process (MDP) formulations of multistage optimization problems when the involved probability distributions are not known exactly, but rather are assumed to belong to specified ambiguity families. The aim of this paper is to clarify a connection between such distributionally robust approaches to multistage stochastic optimization. … Read more
We study a model for adversarial classification based on distributionally robust chance constraints. We show that under Wasserstein ambiguity, the model aims to minimize the conditional value-at-risk of the distance to misclassification, and we explore links to adversarial classification models proposed earlier and to maximum-margin classifiers. We also provide a reformulation of the distributionally robust … Read more
We consider exact deterministic mixed-integer programming (MIP) reformulations of distributionally robust chance-constrained programs (DR-CCP) with random right-hand sides over Wasserstein ambiguity sets. The existing MIP formulations are known to have weak continuous relaxation bounds, and, consequently, for hard instances with small radius, or with a large number of scenarios, the branch-and-bound based solution processes suffer … Read more
We consider stochastic optimization problems in which we aim to minimize the expected value of an objective function with respect to an unknown distribution of random parameters. We analyse the out-of-sample performance of solutions obtained by solving a distributionally robust version of the sample average approximation problem for unconstrained quadratic problems, and derive conditions under … Read more
In this tutorial we discuss several aspects of modeling and solving multistage stochastic programming problems. In particular we discuss distributionally robust and risk averse approaches to multistage stochastic programming, and the involved concept of time consistency. This tutorial is aimed at presenting a certain point of view of multistage stochastic programming, and can be viewed … Read more
In this paper, we investigate optimal policies of distributionally robust (risk averse) inventory models. We demonstrate that if the respective risk measures are not strictly monotone, then there may exist infinitely many optimal policies which are not base-stock and not time consistent. This is in a sharp contrast with the risk neutral formulation of the … Read more