Data Pooling in Stochastic Optimization

Managing large-scale systems often involves simultaneously solving thousands of unrelated stochastic optimization problems, each with limited data. Intuition suggests that one can decouple these problems and solve them separately without loss generality. We propose a novel data-pooling algorithm called Shrunken-SAA disproves this intuition. In particular, we prove combining data across outperform decoupling, even when there is no priori structure linking the are drawn independently. Our approach does not require strong distributional assumptions applies to constrained, possibly nonconvex, nonsmooth such as vehicle-routing, economic lot-sizing, or facility location. compare contrast our results similar phenomenon in statistics (Stein’s phenomenon), highlighting unique features arise setting present estimation. further that, number grows large, learns if pooling improve upon decoupling optimal amount pool, average per problem fixed bounded. Importantly, highlight simple intuition based on stability highlights why offers benefit, elucidating perhaps surprising phenomenon. This most benefits many which has small relevant Finally, demonstrate practical using real from chain retail drug stores context inventory management. paper was accepted by Chung Piaw Teo, Management Science Special Section Data-Driven Prescriptive Analytics.