Structured ambiguity sets for distributionally robust optimization

Abstract: Distributionally robust optimization (DRO) incorporates robustness against uncertainty in the specification of probabilistic models. This paper focuses on mitigating the curse of dimensionality in data-driven DRO problems with optimal transport ambiguity sets. By exploiting independence across lower-dimensional components of the uncertainty, we construct structured ambiguity sets that exhibit a faster shrinkage as the number of collected samples increases. This narrows down the plausible models of the data-generating distribution and mitigates the conservativeness that the decisions of DRO problems over such ambiguity sets may face. We establish statistical guarantees for these structured ambiguity sets and provide dual reformulations of their associated DRO problems for a wide range of objective functions. The benefits of the approach are demonstrated in a numerical example.