# Outlier-Robust Wasserstein DRO

arXiv: https://arxiv.org/abs/2311.05573 · HTML: https://mlsanity.com/paper/2311.05573/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 59 references that are in the map.
- First posted on arXiv 9 Nov 2023.

## Builds on (most cited first, 30 of 34)

- [Generalizing to Unseen Domains via Adversarial Data Augmentation](https://mlsanity.com/paper/1805.12018/) (2018)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [On the Convergence and Robustness of Adversarial Training](https://mlsanity.com/paper/2112.08304/) (2021)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [Recent Advances in Algorithmic High-Dimensional Robust Statistics](https://mlsanity.com/paper/1911.05911/) (2019)
- [Being Robust (in High Dimensions) Can Be Practical](https://mlsanity.com/paper/1703.00893/) (2017)
- [Regularization via Mass Transportation](https://mlsanity.com/paper/1710.10016/) (2017)
- [DORO: Distributional and Outlier Robust Optimization](https://mlsanity.com/paper/2106.06142/) (2021)
- [Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionality](https://mlsanity.com/paper/2009.04382/) (2020)
- [Robust and Heavy-Tailed Mean Estimation Made Simple, via Regret Minimization](https://mlsanity.com/paper/2007.15839/) (2020)
- [Resilience: A Criterion for Learning in the Presence of Arbitrary Outliers](https://mlsanity.com/paper/1703.04940/) (2017)
- [Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spaces](https://mlsanity.com/paper/1804.10556/) (2018)
- [High-Dimensional Robust Mean Estimation in Nearly-Linear Time](https://mlsanity.com/paper/1811.09380/) (2018)
- [Generalized Resilience and Robust Statistics](https://mlsanity.com/paper/1909.08755/) (2019)
- [Theoretical Analysis of Adversarial Learning: A Minimax Approach](https://mlsanity.com/paper/1811.05232/) (2018)
- [Robust Hypothesis Testing Using Wasserstein Uncertainty Sets](https://mlsanity.com/paper/1805.10611/) (2018)
- [Outlier-Robust Optimal Transport: Duality, Structure, and Statistical Analysis](https://mlsanity.com/paper/2111.01361/) (2021)
- [Confidence Regions in Wasserstein Distributionally Robust Estimation](https://mlsanity.com/paper/1906.01614/) (2019)
- [Distributionally robust stochastic programs with side information based on trimmings -- Extended version](https://mlsanity.com/paper/2009.10592/) (2020)
- [Holistic Robust Data-Driven Decisions](https://mlsanity.com/paper/2207.09560/) (2022)
- [Wasserstein Distributionally Robust Kalman Filtering](https://mlsanity.com/paper/1809.08830/) (2018)
- [Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator](https://mlsanity.com/paper/1805.07194/) (2018)
- [On Distributionally Robust Chance Constrained Programs with Wasserstein Distance](https://mlsanity.com/paper/1806.07418/) (2018)
- [Principled learning method for Wasserstein distributionally robust optimization with local perturbations](https://mlsanity.com/paper/2006.03333/) (2020)
- [A Unified Theory of Robust and Distributionally Robust Optimization via the Primal-Worst-Equals-Dual-Best Principle](https://mlsanity.com/paper/2105.00760/) (2021)
- [Bridging Bayesian and Minimax Mean Square Error Estimation via Wasserstein Distributionally Robust Optimization](https://mlsanity.com/paper/1911.03539/) (2019)
- [Certified Robust Neural Networks: Generalization and Corruption Resistance](https://mlsanity.com/paper/2303.02251/) (2023)

## Built on by (most cited first, 16 of 16)

- [Generalized Sobolev Transport for Probability Measures on a Graph](https://mlsanity.com/paper/2402.04516/) (2024)
- [PSL: Rethinking and Improving Softmax Loss from Pairwise Perspective for Recommendation](https://mlsanity.com/paper/2411.00163/) (2024)
- [A New Robust Partial p-Wasserstein-Based Metric for Comparing Distributions](https://mlsanity.com/paper/2405.03664/) (2024)
- [Robust Distribution Learning with Local and Global Adversarial Corruptions](https://mlsanity.com/paper/2406.06509/) (2024)
- [DRO: A Python Library for Distributionally Robust Optimization in Machine Learning](https://mlsanity.com/paper/2505.23565/) (2025)
- [Improved Stochastic Optimization of LogSumExp](https://mlsanity.com/paper/2509.24894/) (2025)
- [Decision Making under Model Misspecification: DRO with Robust Bayesian Ambiguity Sets](https://mlsanity.com/paper/2505.03585/) (2025)
- [Automatic Outlier Rectification via Optimal Transport](https://mlsanity.com/paper/2403.14067/) (2024)
- [On the KL-Divergence-based Robust Satisficing Model](https://mlsanity.com/paper/2408.09157/) (2024)
- [FDR-SVM: A Federated Distributionally Robust Support Vector Machine via a Mixture of Wasserstein Balls Ambiguity Set](https://mlsanity.com/paper/2410.03877/) (2024)
- [Distributionally Robust Optimization with Adversarial Data Contamination](https://mlsanity.com/paper/2507.10718/) (2025)
- [Distributionally Robust Federated Learning with Outlier Resilience](https://mlsanity.com/paper/2509.24462/) (2025)
- [Estimation of Stochastic Optimal Transport Maps](https://mlsanity.com/paper/2512.09499/) (2025)
- [Bulk-Calibrated Credal Ambiguity Sets: Fast, Tractable Decision Making under Out-of-Sample Contamination](https://mlsanity.com/paper/2601.21324/) (2026)
- [Correct and Weight: A Simple Yet Effective Loss for Implicit Feedback Recommendation](https://mlsanity.com/paper/2601.04291/) (2026)
- [Risk-Averse Wasserstein Distributionally Robust Online Learning](https://mlsanity.com/paper/2602.20403/) (2026)

## Abstract (arXiv)

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.