# Wasserstein distributionally robust optimization and its tractable regularization formulations

arXiv: https://arxiv.org/abs/2402.03942 · HTML: https://mlsanity.com/paper/2402.03942/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2024.

## Built on by (most cited first, 5 of 5)

- [Distributionally Robust Optimization with Adversarial Data Contamination](https://mlsanity.com/paper/2507.10718/) (2025)
- [Enhancing Distributional Robustness in Principal Component Analysis by Wasserstein Distances](https://mlsanity.com/paper/2503.02494/) (2025)
- [Wasserstein Distributionally Robust Optimization Through the Lens of Structural Causal Models and Individual Fairness](https://mlsanity.com/paper/2509.26275/) (2025)
- [Tight Robustness Certificates and Wasserstein Distributional Attacks for Deep Neural Networks](https://mlsanity.com/paper/2510.10000/) (2025)
- [Concave Certificates: Geometric Framework for Distributionally Robust Risk and Complexity Analysis](https://mlsanity.com/paper/2601.01311/) (2026)

## Abstract (arXiv)

We study a variety of Wasserstein distributionally robust optimization (WDRO) problems where the distributions in the ambiguity set are chosen by constraining their Wasserstein discrepancies to the empirical distribution. Using the notion of weak Lipschitz property, we derive lower and upper bounds of the corresponding worst-case loss quantity and propose sufficient conditions under which this quantity coincides with its regularization scheme counterpart. Our constructive methodology and elementary analysis also directly characterize the closed-form of the approximate worst-case distribution. Extensive applications show that our theoretical results are applicable to various problems, including regression, classification and risk measure problems.