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Statistical Guarantees for Distributionally Robust Optimization with Optimal Transport and OT-Regularized Divergences

arXiv 2603.27871 ↗First posted 29 Mar 2026stat.ML cs.LGcited by 0

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Abstract (arXiv)

We study finite-sample statistical performance guarantees for distributionally robust optimization (DRO) with optimal transport (OT) and OT-regularized divergence model neighborhoods. Specifically, we derive concentration inequalities for supervised learning via DRO-based adversarial training, as commonly employed to enhance the adversarial robustness of machine learning models. Our results apply to a wide range of OT cost functions, beyond the p-Wasserstein case studied by previous authors. In particular, our results are the first to: 1) cover soft-constraint norm-ball OT cost functions; soft-constraint costs have been shown empirically to enhance robustness when used in adversarial training, 2) apply to the combination of adversarial sample generation and adversarial reweighting that is induced by using OT-regularized f-divergence model neighborhoods; the added reweighting mechanism has also been shown empirically to further improve performance. In addition, even in the p-Wasserstein case, our bounds exhibit better behavior as a function of the DRO neighborhood size than previous results when applied to the adversarial setting.

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References · 31

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19 more
  1. 2020Adversarial Distributional Training for Robust Deep Learningcited by 79
  2. 2019Distributionally Robust Optimization and Generalization in Kernel Methodscited by 73
  3. 2020Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionalitycited by 49
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  6. 2016Recovering Best Statistical Guarantees via the Empirical Divergence-based Distributionally Robust Optimizationcited by 33
  7. 2021Statistical Analysis of Wasserstein Distributionally Robust Estimatorscited by 27
  8. 2019Confidence Regions in Wasserstein Distributionally Robust Estimationcited by 24
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  10. 2016The Empirical Likelihood Approach to Quantifying Uncertainty in Sample Average Approximationcited by 12
  11. 2022A Short and General Duality Proof for Wasserstein Distributionally Robust Optimizationcited by 12
  12. 2022Regularization for Wasserstein Distributionally Robust Optimizationcited by 9
  13. 2023Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Modelscited by 9
  14. 2023Smoothed f-Divergence Distributionally Robust Optimizationcited by 7
  15. 2022Wasserstein Distributionally Robust Estimation in High Dimensions: Performance Analysis and Optimal Hyperparameter Tuningcited by 6
  16. 2022On Generalization and Regularization via Wasserstein Distributionally Robust Optimizationcited by 6
  17. 2022A General Wasserstein Framework for Data-driven Distributionally Robust Optimization: Tractability and Applicationscited by 2
  18. 2023Optimal Transport Regularized Divergences: Application to Adversarial Robustnesscited by 2
  19. 2024Statistical Error Bounds for GANs with Nonlinear Objective Functionalscited by 2

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