Efficient Algorithms for Distributionally Robust Stochastic Optimization with Discrete Scenario Support

Recently, there has been a growing interest in distributionally robust optimization (DRO) as principled approach to data-driven decision making. In this paper, we consider two-stage stochastic problem with discrete scenario support. While much research effort devoted tractable reformulations for DRO problems, especially those continuous support, few efficient numerical algorithms were developed, and most of them can neither handle the non-smooth second-stage cost function nor large number scenarios $K$ effectively. We fill gap by reformulating trilinear min-max-max saddle point developing novel that achieve an $\mathcal{O}(1/\epsilon)$ iteration complexity which only mildly depends on $K$. The major computations involved each these be conducted parallel if necessary. Besides, solving important class problems Kantorovich ball ambiguity set, propose slight modification our avoid expensive computation probability vector projection at price $\mathcal{O}(\sqrt{K})$ times more iterations. Finally, preliminary experiments are demonstrate empirical advantages proposed algorithms.