Robust Two-Stage Optimization with Covariate Data

We consider a generalization of two-stage decision problems in which the second-stage decision may be a function of a predictive signal but cannot adapt fully to the realized uncertainty. We will show how such problems can be learned from sample data by considering a family of regularized sample average formulations. Furthermore, our regularized data-driven formulations admit convex distributionally robust counterparts which enjoy desirable asymptotic out-of-sample performance guarantees. Finally, we show that all derived data-driven formulations can be solved efficiently using canonical stochastic gradient algorithms.