We present a short and elementary proof of the duality for Wasserstein distributionally robust optimization, which holds for any arbitrary Kantorovich transport distance, measurable loss function and nominal probability distribution, so long as certain interchangeability condition holds. As an illustration of the greater generality, we provide a rigorous treatment for duality results in distributionally robust Markov decision processes and distributionally robust stochastic programming.

翻译：只要某些可互换性条件可以维持,瓦森斯坦(Wasserstein)的分布强力优化(Wasserstein)就具有双重性。 只要存在某些可互换性条件,它就具有任意的康托罗维奇(Kantorovich)运输距离、可衡量的损失函数和名义概率分布(名义概率分布 ) 的双重性。 作为更普遍性的例证,我们严格对待分布强的马尔科夫(Markov)决策流程和分布稳健的随机编程的双重性结果。