First-Order Methods for Wasserstein Distributionally Robust Constrained Optimization
Abstract
We consider constrained problems in which input data are affected by errors. In such settings, Wasserstein distributionally robust optimization provides a principled framework to mitigate model risk by optimizing against worst-case data distributions within Wasserstein ambiguity sets. However, the numerical resolution of the resulting problems remains challenging, especially in constrained settings. In this paper, we provide a general, practical way to solve Wasserstein distributionally robust formulations in the presence of constraints. Our approach only requires a linear minimization oracle for the feasible set, and combines two key ingredients: (i) an entropic regularization of the distributionally robust value function, which makes it possible to compute stochastic gradient estimators, and (ii) a stochastic Frank-Wolfe algorithm, which minimizes the regularized robust objective while naturally handling constraints. We illustrate the method, its tractability, and its interests against empirical risk minimization, on two problems: the traffic assignment and the minimum quadratic spanning tree.
Related
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BibTeX
@misc{villuendas2026firstorder,
title = {{First-Order Methods for Wasserstein Distributionally Robust Constrained Optimization}},
author = {Hubert Villuendas and Mathieu Besançon and Jérôme Malick},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.11460},
eprint = {2607.11460},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.11460},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - First-Order Methods for Wasserstein Distributionally Robust Constrained Optimization
AU - Hubert Villuendas
AU - Mathieu Besançon
AU - Jérôme Malick
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2607.11460
UR - https://arxiv.org/abs/2607.11460
AB - We consider constrained problems in which input data are affected by errors. In such settings, Wasserstein distributionally robust optimization provides a principled framework to mitigate model risk by optimizing against worst-case data distributions within Wasserstein ambiguity sets. However, the numerical resolution of the resulting problems remains challenging, especially in constrained settings. In this paper, we provide a general, practical way to solve Wasserstein distributionally robust formulations in the presence of constraints. Our approach only requires a linear minimization oracle for the feasible set, and combines two key ingredients: (i) an entropic regularization of the distributionally robust value function, which makes it possible to compute stochastic gradient estimators, and (ii) a stochastic Frank-Wolfe algorithm, which minimizes the regularized robust objective while naturally handling constraints. We illustrate the method, its tractability, and its interests against empirical risk minimization, on two problems: the traffic assignment and the minimum quadratic spanning tree.
ER -