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, and business analytics. Despite its recent empirical success, existing performance guarantees for generic problems are not yet satisfactory. In this paper, we develop the first finite-sample guarantee without suffering from the curse of dimensionality, which describes how the out-of-sample performance of a robust solution depends on the sample size, dimension of the uncertainty, and the complexity of the loss function class in a nearly optimal way.