# Regularization for Wasserstein Distributionally Robust Optimization

arXiv: https://arxiv.org/abs/2205.08826 · HTML: https://mlsanity.com/paper/2205.08826/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 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)
- [Wasserstein Distributionally Robust Policy Evaluation and Learning for Contextual Bandits](https://mlsanity.com/paper/2309.08748/) (2023)
- [Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Models](https://mlsanity.com/paper/2305.17076/) (2023)
- [Universal generalization guarantees for Wasserstein distributionally robust models](https://mlsanity.com/paper/2402.11981/) (2024)
- [Non-Convex Robust Hypothesis Testing using Sinkhorn Uncertainty Sets](https://mlsanity.com/paper/2403.14822/) (2024)
- [Nested Stochastic Algorithm for Generalized Sinkhorn distance-Regularized Distributionally Robust Optimization](https://mlsanity.com/paper/2503.22923/) (2025)
- [Optimal Transport Regularized Divergences: Application to Adversarial Robustness](https://mlsanity.com/paper/2309.03791/) (2023)
- [Evaluating Black-Box Vulnerabilities with Wasserstein-Constrained Data Perturbations](https://mlsanity.com/paper/2603.15867/) (2026)
- [Statistical Guarantees for Distributionally Robust Optimization with Optimal Transport and OT-Regularized Divergences](https://mlsanity.com/paper/2603.27871/) (2026)

## Abstract (arXiv)

Optimal transport has recently proved to be a useful tool in various machine learning applications needing comparisons of probability measures. Among these, applications of distributionally robust optimization naturally involve Wasserstein distances in their models of uncertainty, capturing data shifts or worst-case scenarios. Inspired by the success of the regularization of Wasserstein distances in optimal transport, we study in this paper the regularization of Wasserstein distributionally robust optimization. First, we derive a general strong duality result of regularized Wasserstein distributionally robust problems. Second, we refine this duality result in the case of entropic regularization and provide an approximation result when the regularization parameters vanish.