Tractable reformulations of DRO problems over structured optimal transport ambiguity sets

Abstract: Structuring ambiguity sets in Wasserstein-based distributionally robust optimization (DRO) can improve their statistical properties when the uncertainty consists of multiple independent components. The aim of this paper is to solve stochastic optimization problems with unknown uncertainty when we only have access to a finite set of samples from it. Exploiting strong duality of DRO problems over structured ambiguity sets, we derive tractable reformulations for certain classes of DRO and uncertainty quantification problems. We also derive tractable reformulations for distributionally robust chance-constrained problems. As the complexity of the reformulations may grow exponentially with the number of independent uncertainty components, we employ clustering strategies to obtain informative estimators, which yield problems of manageable complexity. We demonstrate the effectiveness of the theoretical results in a numerical simulation example.