# Wasserstein Distributionally Robust Optimization and Variation Regularization

arXiv: https://arxiv.org/abs/1712.06050 · HTML: https://mlsanity.com/paper/1712.06050/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2017.

## Built on by (most cited first, 25 of 25)

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- [Diagnosing Model Performance Under Distribution Shift](https://mlsanity.com/paper/2303.02011/) (2023)
- [Statistical Analysis of Wasserstein Distributionally Robust Estimators](https://mlsanity.com/paper/2108.02120/) (2021)
- [Fast Distributionally Robust Learning with Variance Reduced Min-Max Optimization](https://mlsanity.com/paper/2104.13326/) (2021)
- [Distributionally Robust Bayesian Optimization with varphi-divergences](https://mlsanity.com/paper/2203.02128/) (2022)
- [Poisoning Attack against Estimating from Pairwise Comparisons](https://mlsanity.com/paper/2107.01854/) (2021)
- [Learning quantum data with the quantum Earth Mover's distance](https://mlsanity.com/paper/2101.03037/) (2021)
- [Global-Local Regularization Via Distributional Robustness](https://mlsanity.com/paper/2203.00553/) (2022)
- [Learning and Decision-Making with Data: Optimal Formulations and Phase Transitions](https://mlsanity.com/paper/2109.06911/) (2021)
- [Coresets for Wasserstein Distributionally Robust Optimization Problems](https://mlsanity.com/paper/2210.04260/) (2022)
- [Optimal Transport Model Distributional Robustness](https://mlsanity.com/paper/2306.04178/) (2023)
- [Evaluating Model Performance Under Worst-case Subpopulations](https://mlsanity.com/paper/2407.01316/) (2024)
- [Distributionally Robust Prescriptive Analytics with Wasserstein Distance](https://mlsanity.com/paper/2106.05724/) (2021)
- [Learning Invariant Representations under General Interventions on the Response](https://mlsanity.com/paper/2208.10027/) (2022)
- [Distributionally Robust Multiclass Classification and Applications in Deep Image Classifiers](https://mlsanity.com/paper/2109.12772/) (2021)
- [Human Imperceptible Attacks and Applications to Improve Fairness](https://mlsanity.com/paper/2111.15603/) (2021)
- [Promoting Ensemble Diversity with Interactive Bayesian Distributional Robustness for Fine-tuning Foundation Models](https://mlsanity.com/paper/2506.07247/) (2025)
- [Distributionally Robust Multi-Output Regression Ranking](https://mlsanity.com/paper/2109.12803/) (2021)
- [Distributionally Robust Multiclass Classification and Applications in Deep Image Classifiers](https://mlsanity.com/paper/2210.08198/) (2022)
- [Optimize-via-Predict: Realizing out-of-sample optimality in data-driven optimization](https://mlsanity.com/paper/2309.11147/) (2023)
- [Decision-Driven Regularization: A Blended Model for Learning and Optimization](https://mlsanity.com/paper/2608.15124/) (2026)

## Abstract (arXiv)

Wasserstein distributionally robust optimization (DRO) has recently achieved empirical success for various applications in operations research and machine learning, owing partly to its regularization effect. Although connection between Wasserstein DRO and regularization has been established in several settings, existing results often require restrictive assumptions, such as smoothness or convexity, that are not satisfied for many problems. In this paper, we develop a general theory on the variation regularization effect of the Wasserstein DRO - a new form of regularization that generalizes total-variation regularization, Lipschitz regularization and gradient regularization. Our results cover possibly non-convex and non-smooth losses and losses on non-Euclidean spaces. Examples include multi-item newsvendor, portfolio selection, linear prediction, neural networks, manifold learning, and intensity estimation for Poisson processes, etc. As an application of our theory of variation regularization, we derive new generalization guarantees for adversarial robust learning.