论文标题
Wasserstein分布强劲优化的简短且一般的二元性证明
A Short and General Duality Proof for Wasserstein Distributionally Robust Optimization
论文作者
论文摘要
我们为Wasserstein分布鲁棒优化提供了一般的二元性结果，该优化适用于任何Kantorovich运输成本，可测量的损失函数和名义概率分布。假设现有二元性结果固有的互换性原理，我们的证明只使用一维凸分析。此外，我们证明，当且仅当满足某些可测量的投影和弱可测量的选择条件时，互换性原理才能保持。为了说明我们方法的更广泛的适用性，我们提供了对二元性的严格处理，导致马尔可夫决策过程和分布强大的多阶段随机编程。此外，我们将分析扩展到其他问题，例如Infinity-Wassestein分布在强大的优化，规避风险的优化和全球化的分布在稳健方面。
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.
