Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionality

Wasserstein distributionally robust optimization is a recent emerging modeling paradigm for decision making under data uncertainty. Because of its computational tractability and interpretability, it has achieved great empirical successes across several application domains in operations research, computer science, engineering, business analytics. Despite success, existing performance guarantees generic problems are not yet satisfactory. In this paper, we develop the first finite-sample guarantee without suffering from curse dimensionality, which describes how out-of-sample solution depends on sample size, dimension uncertainty, complexity loss function class nearly optimal way.