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Distributionally Robust Convex Optimization

Wolfram Wiesemann (ww***at***imperial.ac.uk)
Daniel Kuhn (dkuhn***at***imperial.ac.uk)
Melvyn Sim (melvynsim***at***nus.edu.sg)

Abstract: Distributionally robust optimization is a paradigm for decision-making under uncertainty where the uncertain problem data is governed by a probability distribution that is itself subject to uncertainty. The distribution is then assumed to belong to an ambiguity set comprising all distributions that are compatible with the decision maker's prior information. In this paper, we propose a unifying framework for modeling and solving distributionally robust optimization problems. We introduce standardized ambiguity sets that contain all distributions with prescribed conic representable confidence sets and with mean values residing on an affine manifold. These ambiguity sets are highly expressive and encompass many ambiguity sets from the recent literature as special cases. They also allow us to characterize distributional families in terms of several classical and/or robust statistical indicators that have not yet been studied in the context of robust optimization. We determine sharp conditions under which distributionally robust optimization problems based on our standardized ambiguity sets are computationally tractable. We also provide tractable conservative approximations for problems that violate these conditions.

Keywords: Robust optimization, ambiguous probability distributions, conic optimization

Category 1: Robust Optimization

Category 2: Stochastic Programming

Category 3: Convex and Nonsmooth Optimization (Convex Optimization )

Citation:

Download: [Compressed Postscript][PDF]

Entry Submitted: 02/04/2013
Entry Accepted: 02/04/2013
Entry Last Modified: 09/30/2013

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