# On Generalization and Regularization via Wasserstein Distributionally Robust Optimization

arXiv: https://arxiv.org/abs/2212.05716 · HTML: https://mlsanity.com/paper/2212.05716/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 64 references that are in the map.
- First posted on arXiv 12 Dec 2022.

## Builds on (most cited first, 9 of 9)

- [Generalizing to Unseen Domains via Adversarial Data Augmentation](https://mlsanity.com/paper/1805.12018/) (2018)
- [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)
- [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)
- [Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionality](https://mlsanity.com/paper/2009.04382/) (2020)
- [Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances](https://mlsanity.com/paper/1802.04885/) (2018)
- [Confidence Regions in Wasserstein Distributionally Robust Estimation](https://mlsanity.com/paper/1906.01614/) (2019)

## Built on by (most cited first, 6 of 6)

- [Robust Distribution Learning with Local and Global Adversarial Corruptions](https://mlsanity.com/paper/2406.06509/) (2024)
- [Optimal Transport Regularized Divergences: Application to Adversarial Robustness](https://mlsanity.com/paper/2309.03791/) (2023)
- [Adjusted Wasserstein Distributionally Robust Estimator in Statistical Learning](https://mlsanity.com/paper/2303.15579/) (2023)
- [Wasserstein Distributionally Robust Optimization Through the Lens of Structural Causal Models and Individual Fairness](https://mlsanity.com/paper/2509.26275/) (2025)
- [Statistical Guarantees for Distributionally Robust Optimization with Optimal Transport and OT-Regularized Divergences](https://mlsanity.com/paper/2603.27871/) (2026)
- [Distributionally robust linear regression through the lens of adversarial training](https://mlsanity.com/paper/2609.39449/) (2026)

## Abstract (arXiv)

Wasserstein distributionally robust optimization (DRO) has gained prominence in operations research and machine learning as a powerful method for achieving solutions with favorable out-of-sample performance. Two compelling explanations for its success are the generalization bounds derived from Wasserstein DRO and its equivalence to regularization schemes commonly used in machine learning. However, existing results on generalization bounds and regularization equivalence are largely limited to settings where the Wasserstein ball is of a specific type, and the decision criterion takes certain forms of expected functions. In this paper, we show that generalization bounds and regularization equivalence can be obtained in a significantly broader setting, where the Wasserstein ball is of a general type and the decision criterion accommodates any form, including general risk measures. This not only addresses important machine learning and operations management applications but also expands to general decision-theoretical frameworks previously unaddressed by Wasserstein DRO. Our results are strong in that the generalization bounds do not suffer from the curse of dimensionality and the equivalency to regularization is exact. As a by-product, we show that Wasserstein DRO coincides with the recent max-sliced Wasserstein DRO for it any decision criterion under affine decision rules -- resulting in both being efficiently solvable as convex programs via our general regularization results. These general assurances provide a strong foundation for expanding the application of Wasserstein DRO across diverse domains of data-driven decision problems.