Outlier-Robust Wasserstein DRO

TL;DR

This paper introduces a novel outlier-robust Wasserstein DRO framework that effectively handles both geometric and non-geometric data perturbations, including adversarial outliers, with theoretical guarantees and practical algorithms.

Contribution

It proposes a new robust Wasserstein DRO method that accounts for data contamination, deriving minimax optimal risk bounds and providing tractable convex reformulations.

Findings

The method achieves robustness against adversarial outliers.

Theoretical risk bounds are derived for the proposed framework.

Experiments validate improved performance on regression and classification tasks.

Abstract

Distributionally robust optimization (DRO) is an effective approach for data-driven decision-making in the presence of uncertainty. Geometric uncertainty due to sampling or localized perturbations of data points is captured by Wasserstein DRO (WDRO), which seeks to learn a model that performs uniformly well over a Wasserstein ball centered around the observed data distribution. However, WDRO fails to account for non-geometric perturbations such as adversarial outliers, which can greatly distort the Wasserstein distance measurement and impede the learned model. We address this gap by proposing a novel outlier-robust WDRO framework for decision-making under both geometric (Wasserstein) perturbations and non-geometric (total variation (TV)) contamination that allows an $\varepsilon$-fraction of data to be arbitrarily corrupted. We design an uncertainty set using a certain robust Wasserstein ball that accounts for both perturbation types and derive minimax optimal excess risk bounds for this procedure that explicitly capture the Wasserstein and TV risks. We prove a strong duality result that enables tractable convex reformulations and efficient computation of our outlier-robust WDRO problem. When the loss function depends only on low-dimensional features of the data, we eliminate certain dimension dependencies from the risk bounds that are unavoidable in the general setting. Finally, we present experiments validating our theory on standard regression and classification tasks.