Data-Driven Two-Stage Stochastic Programming with Marginal Data

We present new methodologies to solve data-driven two-stage stochastic optimization when only the marginal data are available. We propose a novel data-driven distributionally robust framework that only uses the available marginal data. The proposed model is distinguished from the traditional techniques of solving missing data in that it conducts an integrated analysis of missing data and optimization problems, whereas classical methods conduct separate analyses by first recovering the missing data and then finding the optimal solutions. On the theoretical side, we show that our model produces risk-averse solutions and guarantees finite sample performance. Empirical experiments are conducted on two applications based on synthetic data and real-world data. We validate the proposed finite sample guarantee and show that the proposed approach achieves better out-of-sample performance and higher reliability than the classical data imputation-based approach.