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Rui Gao (rgao32gatech.edu) Abstract: Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is an underlying probability distribution that is known exactly, one hedges against a chosen set of distributions. In this paper, we consider sets of distributions that are within a chosen Wasserstein distance from a nominal distribution. We argue that such a choice of sets has two advantages: (1) The resulting distributions hedged against are more reasonable than those resulting from other popular choices of sets, such as Φdivergence ambiguity set. (2) The problem of determining the worstcase expectation has desirable tractability properties. We derive a dual reformulation of the corresponding DRSO problem and construct approximate worstcase distributions (or an exact worstcase distribution if it exists) explicitly via the firstorder optimality conditions of the dual problem. Our contributions are fivefold. (i) We identify necessary and sufficient conditions for the existence of a worstcase distribution, which is naturally related to the growth rate of the objective function. (ii) We show that the worstcase distributions resulting from an appropriate Wasserstein distance have a concise structure and a clear interpretation. (iii) Using this structure, we show that datadriven DRSO problems can be approximated to any accuracy by robust optimization problems, and thereby many DRSO problems become tractable by using tools from robust optimization. (iv) To the best of our knowledge, our proof of strong duality is the first constructive proof for DRSO problems, and we show that the constructive proof technique is also useful in other contexts. (v) Our strong duality result holds in a very general setting, and we show that it can be applied to infinite dimensional process control problems and worstcase valueatrisk analysis. Keywords: distributionally robust optimization; datadriven; worstcase distribution; ambiguity set Category 1: Stochastic Programming Category 2: Infinite Dimensional Optimization Category 3: Robust Optimization Citation: Download: [PDF] Entry Submitted: 04/06/2016 Modify/Update this entry  
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