# Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Models

arXiv: https://arxiv.org/abs/2305.17076 · HTML: https://mlsanity.com/paper/2305.17076/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 49 references that are in the map.
- First posted on arXiv 26 May 2023.

## Builds on (most cited first, 26 of 26)

- [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)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Large-Scale Methods for Distributionally Robust Optimization](https://mlsanity.com/paper/2010.05893/) (2020)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [Regularization via Mass Transportation](https://mlsanity.com/paper/1710.10016/) (2017)
- [Distributionally Robust Optimization and Generalization in Kernel Methods](https://mlsanity.com/paper/1905.10943/) (2019)
- [Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionality](https://mlsanity.com/paper/2009.04382/) (2020)
- [Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2109.11926/) (2021)
- [Optimal Transport Based Distributionally Robust Optimization: Structural Properties and Iterative Schemes](https://mlsanity.com/paper/1810.02403/) (2018)
- [Statistical Analysis of Wasserstein Distributionally Robust Estimators](https://mlsanity.com/paper/2108.02120/) (2021)
- [Non-Convex Bilevel Games with Critical Point Selection Maps](https://mlsanity.com/paper/2207.04888/) (2022)
- [Confidence Regions in Wasserstein Distributionally Robust Estimation](https://mlsanity.com/paper/1906.01614/) (2019)
- [Regularized Optimal Transport is Ground Cost Adversarial](https://mlsanity.com/paper/2002.03967/) (2020)
- [Principled learning method for Wasserstein distributionally robust optimization with local perturbations](https://mlsanity.com/paper/2006.03333/) (2020)
- [Semi-supervised Learning based on Distributionally Robust Optimization](https://mlsanity.com/paper/1702.08848/) (2017)
- [Fast Epigraphical Projection-based Incremental Algorithms for Wasserstein Distributionally Robust Support Vector Machine](https://mlsanity.com/paper/2010.12865/) (2020)
- [Generalization Bounds with Minimal Dependency on Hypothesis Class via Distributionally Robust Optimization](https://mlsanity.com/paper/2106.11180/) (2021)
- [A Data-Driven Approach to Robust Hypothesis Testing Using Sinkhorn Uncertainty Sets](https://mlsanity.com/paper/2202.04258/) (2022)
- [Regularization for Wasserstein Distributionally Robust Optimization](https://mlsanity.com/paper/2205.08826/) (2022)
- [Statistical Limit Theorems in Distributionally Robust Optimization](https://mlsanity.com/paper/2303.14867/) (2023)
- [First-order Optimization for Superquantile-based Supervised Learning](https://mlsanity.com/paper/2009.14575/) (2020)
- [Adversarially Robust Kernel Smoothing](https://mlsanity.com/paper/2102.08474/) (2021)
- [Entropy-regularized Wasserstein distributionally robust shape and topology optimization](https://mlsanity.com/paper/2209.01500/) (2022)

## Built on by (most cited first, 9 of 9)

- [Unifying Distributionally Robust Optimization via Optimal Transport Theory](https://mlsanity.com/paper/2308.05414/) (2023)
- [Universal generalization guarantees for Wasserstein distributionally robust models](https://mlsanity.com/paper/2402.11981/) (2024)
- [textttskwdro: a library for Wasserstein distributionally robust machine learning](https://mlsanity.com/paper/2410.21231/) (2024)
- [Wasserstein Distributionally Robust Nonparametric Regression](https://mlsanity.com/paper/2505.07967/) (2025)
- [Mixture Data for Training Cannot Ensure Out-of-distribution Generalization](https://mlsanity.com/paper/2312.16243/) (2023)
- [Provable Robust Overfitting Mitigation in Wasserstein Distributionally Robust Optimization](https://mlsanity.com/paper/2503.04315/) (2025)
- [Distributionally Robust Wireless Semantic Communication with Large AI Models](https://mlsanity.com/paper/2506.03167/) (2025)
- [Unregularized limit of stochastic gradient method for Wasserstein distributionally robust optimization](https://mlsanity.com/paper/2506.04948/) (2025)
- [Statistical Guarantees for Distributionally Robust Optimization with Optimal Transport and OT-Regularized Divergences](https://mlsanity.com/paper/2603.27871/) (2026)

## Abstract (arXiv)

Wasserstein distributionally robust estimators have emerged as powerful models for prediction and decision-making under uncertainty. These estimators provide attractive generalization guarantees: the robust objective obtained from the training distribution is an exact upper bound on the true risk with high probability. However, existing guarantees either suffer from the curse of dimensionality, are restricted to specific settings, or lead to spurious error terms. In this paper, we show that these generalization guarantees actually hold on general classes of models, do not suffer from the curse of dimensionality, and can even cover distribution shifts at testing. We also prove that these results carry over to the newly-introduced regularized versions of Wasserstein distributionally robust problems.