mlsanityData to 14 Oct 2026

Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Models

arXiv 2305.17076 ↗First posted 26 May 2023cs.LG stat.MLcited by 9

Not on the map. Why?

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.

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

26 of 49 references.

References · 26

  1. 2017Certifying Some Distributional Robustness with Principled Adversarial Trainingcited by 337
  2. 2015Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulationscited by 291
  3. 2016Stochastic Optimization for Large-scale Optimal Transportcited by 189
  4. 2016Distributionally Robust Stochastic Optimization with Wasserstein Distancecited by 185
  5. 2020Large-Scale Methods for Distributionally Robust Optimizationcited by 179
  6. 2019Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learningcited by 170
  7. 2015Distributionally Robust Logistic Regressioncited by 126
  8. 2017Regularization via Mass Transportationcited by 81
  9. 2019Distributionally Robust Optimization and Generalization in Kernel Methodscited by 73
  10. 2020Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionalitycited by 49
  11. 2021Sinkhorn Distributionally Robust Optimizationcited by 38
  12. 2018Optimal Transport Based Distributionally Robust Optimization: Structural Properties and Iterative Schemescited by 30
14 more
  1. 2021Statistical Analysis of Wasserstein Distributionally Robust Estimatorscited by 27
  2. 2022Non-Convex Bilevel Games with Critical Point Selection Mapscited by 25
  3. 2019Confidence Regions in Wasserstein Distributionally Robust Estimationcited by 24
  4. 2020Regularized Optimal Transport is Ground Cost Adversarialcited by 17
  5. 2020Principled learning method for Wasserstein distributionally robust optimization with local perturbationscited by 14
  6. 2017Semi-supervised Learning based on Distributionally Robust Optimizationcited by 12
  7. 2020Fast Epigraphical Projection-based Incremental Algorithms for Wasserstein Distributionally Robust Support Vector Machinecited by 10
  8. 2021Generalization Bounds with Minimal Dependency on Hypothesis Class via Distributionally Robust Optimizationcited by 9
  9. 2022A Data-Driven Approach to Robust Hypothesis Testing Using Sinkhorn Uncertainty Setscited by 9
  10. 2022Regularization for Wasserstein Distributionally Robust Optimizationcited by 9
  11. 2023Statistical Limit Theorems in Distributionally Robust Optimizationcited by 7
  12. 2020First-order Optimization for Superquantile-based Supervised Learningcited by 4
  13. 2021Adversarially Robust Kernel Smoothingcited by 4
  14. 2022Entropy-regularized Wasserstein distributionally robust shape and topology optimizationcited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 2; 2025: 4; 2026: 1.

9 papers.

  1. 2023Unifying Distributionally Robust Optimization via Optimal Transport Theorycited by 13
  2. 2024Universal generalization guarantees for Wasserstein distributionally robust modelscited by 5
  3. 2024textttskwdro: a library for Wasserstein distributionally robust machine learningcited by 4
  4. 2025Wasserstein Distributionally Robust Nonparametric Regressioncited by 3
  5. 2023Mixture Data for Training Cannot Ensure Out-of-distribution Generalizationcited by 1
  6. 2025Provable Robust Overfitting Mitigation in Wasserstein Distributionally Robust Optimizationcited by 0
  7. 2025Distributionally Robust Wireless Semantic Communication with Large AI Modelscited by 0
  8. 2025Unregularized limit of stochastic gradient method for Wasserstein distributionally robust optimizationcited by 0
  9. 2026Statistical Guarantees for Distributionally Robust Optimization with Optimal Transport and OT-Regularized Divergencescited by 0