A Short and General Duality Proof for Wasserstein Distributionally Robust Optimization
提出一个简短且通用的对偶证明，基于Legendre-Fenchel对偶，揭示强对偶性依赖于可交换性原理，并推广到风险厌恶优化和全局化分布鲁棒优化。
Wasserstein distributionally robust optimization has emerged as a recent topic with broader applications in operations research and machine learning. Various proofs have been presented in the literature, each differing in assumptions and levels of generality. In “A Short and General Duality Proof for Wasserstein Distributionally Robust Optimization,” Zhang, Yang, and Gao present a novel elementary proof that not only shortens existing frameworks but also offers surprising generalizations. Leveraging classical Legendre—Fenchel duality, they demonstrate that strong duality is contingent on a certain interchangeability principle. Moreover, they extend this duality result to encompass risk-averse optimization and globalized distributionally robust counterparts.