A Simple and General Duality Proof for Wasserstein Distributionally Robust Optimization

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.