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

Understand

Wasserstein distributionally robust optimization (DRO) aims to find robust and generalizable solutions by hedging against data perturbations in Wasserstein distance.

• Despite its recent empirical success in operations research and machine learning, existing performance guarantees for generic loss functions are either overly conservative due to the curse of dimensionality, or plausible only in large sample asymptotics.
• In this paper, we develop a non-asymptotic framework for analyzing the out-of-sample performance for Wasserstein robust learning and the generalization bound for its related Lipschitz and gradient regularization problems.
• To the best of our knowledge, this gives the first finite-sample guarantee for generic Wasserstein DRO problems without suffering from the curse of dimensionality.