A Short and General Duality Proof for Wasserstein Distributionally Robust Optimization

Luhao Zhang (), Jincheng Yang () and Rui Gao ()
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Luhao Zhang: Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, Maryland 21218
Jincheng Yang: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Rui Gao: Department of Information, Risk and Operations Management, The University of Texas at Austin, Austin, Texas 78712

Operations Research, 2025, vol. 73, issue 4, 2146-2155

Abstract: 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, risk-averse optimization, and globalized distributionally robust counterpart.

Keywords: Optimization; Wasserstein metric; distributionally robust optimization; duality (search for similar items in EconPapers)
Date: 2025
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