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.

翻译：本文给出了Wasserstein分布鲁棒优化的一个通用对偶结果，该结果适用于任意Kantorovich运输成本、可测损失函数和名义概率分布。基于现有对偶结果中固有的可交换性原理，我们的证明仅需使用一维凸分析。此外，我们证明了可交换性原理成立当且仅当满足特定的可测投影和弱可测选择条件。为说明本方法的广泛适用性，我们系统处理了分布鲁棒马尔可夫决策过程和分布鲁棒多阶段随机规划中的对偶结果。同时，我们将分析拓展至其他问题，包括无穷Wasserstein分布鲁棒优化、风险厌恶优化及全局化分布鲁棒对应问题。