| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 33 | |
| Number of page(s) | 31 | |
| DOI | https://doi.org/10.1051/cocv/2023019 | |
| Published online | 11 May 2023 | |
Regularization for Wasserstein distributionally robust optimization
1 DI, ENS, Univ. PSL, 75005, Paris, France and
Univ. Grenoble Alpes, 38000 Grenoble, France.
2 Univ. Grenoble Alpes, 38000 Grenoble, France.
3 CNRS & LJK, 38000, Grenoble, France.
* Corresponding author: jerome.malick@univ-grenoble-alpes.fr
Received:
13
January
2022
Accepted:
22
March
2023
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.
Mathematics Subject Classification: 90C17 / 90C25 / 49N15 / 49Q22
Key words: Distributionally robust optimization / optimal transport / duality / entropic regularization
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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