Nash Equilibria, Regularization, and Computation in Optimal Transport-Based Distributionally Robust Optimization

• 成果类型: Article
• 署名作者: Shafiee, Soroosh; Aolaritei, Liviu; Dorller, Florian; Kuhn, Daniel
• 署名单位: Cornell University; University of California System; University of California Berkeley; Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2023.0138
• 发表日期: 2026
• 关键词: distributionally robust optimization; Optimal Transport; regularization; Nash equilibrium

摘要

We study optimal transport-based distributionally robust optimization problems in which a fictitious adversary, often envisioned as nature, can choose the distribution of the uncertain problem parameters by reshaping a prescribed reference distribution at a finite transportation cost. In this framework, we show that robustification is intimately related to various forms of variation and Lipschitz regularization even if the transportation cost function fails to be (some power of) a metric. We also derive conditions for the existence and the computability of a Nash equilibrium between the decision maker and nature, and we demonstrate numerically that nature's Nash strategy can be viewed as a distribution that is supported on remarkably deceptive adversarial samples. Finally, we identify practically relevant classes of optimal transport-based distributionally robust optimization problems that can be addressed with efficient gradient descent algorithms even if the loss function or the transportation cost function is nonconvex (but not both at the same time).