Distributionally Robust Optimization using Cost-Aware Ambiguity Sets

We present a novel class of ambiguity sets for distributionally robust optimization (DRO). These ambiguity sets, called cost-aware ambiguity sets, are defined as halfspaces which depend on the cost function evaluated at an independent estimate of the optimal solution, thus excluding only those distributions that are expected to have significant impact on the obtained worst-case cost. We show that the resulting DRO method provides both a high-confidence upper bound and a consistent estimator of the out-of-sample expected cost, and demonstrate empirically that it results in less conservative solutions compared to divergence-based ambiguity sets.