Distributionally Robust Stochastic Optimization with Wasserstein Distance

Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is a known true underlying probability distribution, one hedges against a chosen set of distributions. In this paper, we first point out that the set of distributions should be chosen to be appropriate for the application at hand and some of the choices that have been popular until recently are, for many applications, not good choices. We next consider sets of distributions that are within a chosen Wasserstein distance from a nominal distribution. Such a choice of sets has two advantages: (1) The resulting distributions hedged against are more reasonable than those…