Principled learning method for Wasserstein distributionally robust optimization with local perturbations

TL;DR

This paper introduces a new principled approach for Wasserstein distributionally robust optimization that ensures risk consistency and extends to local data perturbations, including Mixup, with demonstrated robustness in image classification.

Contribution

It proposes a novel approximation theorem for WDRO, establishes risk consistency, and extends the method to local data perturbations like Mixup.

Findings

Achieves higher accuracy on noisy image datasets

Demonstrates robustness against local data perturbations

Extends WDRO inference to include Mixup as a special case

Abstract

Wasserstein distributionally robust optimization (WDRO) attempts to learn a model that minimizes the local worst-case risk in the vicinity of the empirical data distribution defined by Wasserstein ball. While WDRO has received attention as a promising tool for inference since its introduction, its theoretical understanding has not been fully matured. Gao et al. (2017) proposed a minimizer based on a tractable approximation of the local worst-case risk, but without showing risk consistency. In this paper, we propose a minimizer based on a novel approximation theorem and provide the corresponding risk consistency results. Furthermore, we develop WDRO inference for locally perturbed data that include the Mixup (Zhang et al., 2017) as a special case. We show that our approximation and risk consistency results naturally extend to the cases when data are locally perturbed. Numerical experiments demonstrate robustness of the proposed method using image classification datasets. Our results show that the proposed method achieves significantly higher accuracy than baseline models on noisy datasets.