# Principled learning method for Wasserstein distributionally robust optimization with local perturbations

arXiv: https://arxiv.org/abs/2006.03333 · HTML: https://mlsanity.com/paper/2006.03333/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2020.

## Built on by (most cited first, 14 of 14)

- [Out-of-distribution Detection with Implicit Outlier Transformation](https://mlsanity.com/paper/2303.05033/) (2023)
- [Noisy Feature Mixup](https://mlsanity.com/paper/2110.02180/) (2021)
- [Outlier-Robust Wasserstein DRO](https://mlsanity.com/paper/2311.05573/) (2023)
- [Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Models](https://mlsanity.com/paper/2305.17076/) (2023)
- [Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization](https://mlsanity.com/paper/2303.03900/) (2023)
- [Universal generalization guarantees for Wasserstein distributionally robust models](https://mlsanity.com/paper/2402.11981/) (2024)
- [DRFLM: Distributionally Robust Federated Learning with Inter-client Noise via Local Mixup](https://mlsanity.com/paper/2204.07742/) (2022)
- [DRAUC: An Instance-wise Distributionally Robust AUC Optimization Framework](https://mlsanity.com/paper/2311.03055/) (2023)
- [Wasserstein Distributionally Robust Nonparametric Regression](https://mlsanity.com/paper/2505.07967/) (2025)
- [RogueMerge: Robust and Unified Attacks against LLM Model Merging](https://mlsanity.com/paper/2606.03344/) (2026)
- [Beckman Defense](https://mlsanity.com/paper/2301.01495/) (2023)
- [Distributionally Robust Cross Subject EEG Decoding](https://mlsanity.com/paper/2308.11651/) (2023)
- [Risk-Averse Wasserstein Distributionally Robust Online Learning](https://mlsanity.com/paper/2602.20403/) (2026)
- [Distributionally Robust Set Representation Learning Under Inference-Time Element Corruption](https://mlsanity.com/paper/2605.30089/) (2026)

## Abstract (arXiv)

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.