A Short and General Duality Proof for Wasserstein Distributionally Robust Optimization
成果类型：
Article
署名作者：
Zhang, Luhao; Yang, Jincheng; Gao, Rui
署名单位：
Johns Hopkins University; University of Chicago; University of Texas System; University of Texas Austin
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.2023.0135
发表日期：
2025
页码：
2146-2155
关键词：
摘要：
We present a general duality result for Wasserstein distributionally robust optimization that holds for any Kantorovich transport cost, measurable loss function, and nominal probability distribution. Assuming an interchangeability principle inherent in existing duality results, our proof only uses one-dimensional convex analysis. Furthermore, we demonstrate that the interchangeability principle holds if and only if certain measurable projection and weak measurable selection conditions are satisfied. To illustrate the broader applicability of our approach, we provide a rigorous treatment of duality results in distributionally robust Markov decision processes and distributionally robust multistage stochastic programming. Additionally, we extend our analysis to other problems such as infinity-Wasserstein distributionally robust optimization, riskaverse optimization, and globalized distributionally robust counterpart. Funding: L. Zhang acknowledges the support of Xunyu Zhou and the Nie Center for Intelligent Asset Management at Columbia University. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.0135.