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

arXiv: https://arxiv.org/abs/2603.27871 · HTML: https://mlsanity.com/paper/2603.27871/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 52 references that are in the map.
- First posted on arXiv 29 Mar 2026.

## Builds on (most cited first, 30 of 31)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Practical Black-Box Attacks against Machine Learning](https://mlsanity.com/paper/1602.02697/) (2016)
- [The Limitations of Deep Learning in Adversarial Settings](https://mlsanity.com/paper/1511.07528/) (2015)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Geometry-aware Instance-reweighted Adversarial Training](https://mlsanity.com/paper/2010.01736/) (2020)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Variance-based regularization with convex objectives](https://mlsanity.com/paper/1610.02581/) (2016)
- [Data-Driven Robust Optimization](https://mlsanity.com/paper/1401.0212/) (2013)
- [Regularization via Mass Transportation](https://mlsanity.com/paper/1710.10016/) (2017)
- [Adversarial Distributional Training for Robust Deep Learning](https://mlsanity.com/paper/2002.05999/) (2020)
- [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)
- [A Unified Wasserstein Distributional Robustness Framework for Adversarial Training](https://mlsanity.com/paper/2202.13437/) (2022)
- [Recovering Best Statistical Guarantees via the Empirical Divergence-based Distributionally Robust Optimization](https://mlsanity.com/paper/1605.09349/) (2016)
- [Statistical Analysis of Wasserstein Distributionally Robust Estimators](https://mlsanity.com/paper/2108.02120/) (2021)
- [Confidence Regions in Wasserstein Distributionally Robust Estimation](https://mlsanity.com/paper/1906.01614/) (2019)
- [Unifying Distributionally Robust Optimization via Optimal Transport Theory](https://mlsanity.com/paper/2308.05414/) (2023)
- [The Empirical Likelihood Approach to Quantifying Uncertainty in Sample Average Approximation](https://mlsanity.com/paper/1604.02573/) (2016)
- [A Short and General Duality Proof for Wasserstein Distributionally Robust Optimization](https://mlsanity.com/paper/2205.00362/) (2022)
- [Regularization for Wasserstein Distributionally Robust Optimization](https://mlsanity.com/paper/2205.08826/) (2022)
- [Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Models](https://mlsanity.com/paper/2305.17076/) (2023)
- [Smoothed f-Divergence Distributionally Robust Optimization](https://mlsanity.com/paper/2306.14041/) (2023)
- [Wasserstein Distributionally Robust Estimation in High Dimensions: Performance Analysis and Optimal Hyperparameter Tuning](https://mlsanity.com/paper/2206.13269/) (2022)
- [On Generalization and Regularization via Wasserstein Distributionally Robust Optimization](https://mlsanity.com/paper/2212.05716/) (2022)
- [A General Wasserstein Framework for Data-driven Distributionally Robust Optimization: Tractability and Applications](https://mlsanity.com/paper/2207.09403/) (2022)
- [Optimal Transport Regularized Divergences: Application to Adversarial Robustness](https://mlsanity.com/paper/2309.03791/) (2023)

## 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.