Wasserstein Distributionally Robust Optimization and Variation Regularization

Understand

Wasserstein distributionally robust optimization (DRO) has recently achieved empirical success for various applications in operations research and machine learning, owing partly to its regularization effect.

• Although connection between Wasserstein DRO and regularization has been established in several settings, existing results often require restrictive assumptions, such as smoothness or convexity, that are not satisfied for many problems.
• In this paper, we develop a general theory on the variation regularization effect of the Wasserstein DRO - a new form of regularization that generalizes total-variation regularization, Lipschitz regularization and gradient regularization.
• Our results cover possibly non-convex and non-smooth losses and losses on non-Euclidean spaces.