Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets

We consider a distributionally robust optimization problem where the ambiguity set of probability distributions is characterized by a tractable conic representable support set and by expectation constraints. We propose a new class of infinitely constrained ambiguity sets for which the number of expectation constraints could be infinite. The description of such ambiguity sets can incorporate the stochastic dominance, dispersion, fourth moment, and our newly proposed “entropic dominance” information about the uncertainty. In particular, we demonstrate that including this entropic dominance can improve the characterization of stochastic independence as compared with a characterization based solely on covariance information. Because the corresponding distributionally robust optimization problem need not lead to tractable reformulations, we adopt a greedy improvement procedure that consists of solving a sequence of tractable distributionally robust optimization subproblems—each of which considers a relaxed and finitely constrained ambiguity set. Our computational study establishes that this approach converges reasonably well.