Tractable Distributionally Robust Optimization with Data

We present a unified and tractable framework for distributionally robust optimization that could encompass a variety of statistical information including, among others things, constraints on expectation, conditional expectation, and disjoint confidence sets with uncertain probabilities defined by φ-divergence. In particular, we also show that the Wasserstein-based ambiguity set has an equivalent formulation via our proposed ambiguity set, which would enable us to tractably approximate a Wasserstein-based distributionally robust optimization problem with recourse. To address a distributionally robust optimization problem with recourse, we introduce the tractable adaptive recourse scheme (TARS), which is based on the classical linear decision rule and can also be applied in situations where the recourse decisions are discrete. We demonstrate the effectiveness of the TARS in our computational study on a multi-item newsvendor problem.