Wasserstein-Distance Distributionally Robust Optimization

Wasserstein distance can measure the distance between probability distributions and it is closely related to the optimal transport problem. This chapter focuses on Wasserstein-distance distributionally robust optimization. We first provide an overview of Wasserstein distance to establish an intuition about what a Wasserstein-distance ambiguity set should be like. Subsequently, Wasserstein-distance ambiguity sets of discrete and general probability distributions are both defined, with discussions about the parameter choice. Finally, the reformulation methods of worst-case expectations and robust chance constraints are introduced.