Data-Driven Solutions and Uncertainty Quantification for Multistage Stochastic Optimization

Multistage stochastic optimization problems appear commonly in various disciplines in operations management and system control. While computational methods have been studied, they are mostly restricted to two-stage problems or otherwise require strong assumptions. In this paper, we propose a simple data-driven solution technique and uncertainty quantification method for these problems, based on natural multisample generalizations of the well-known sample average approximation and the so-called single replication procedure. Under the assumptions of stagewise independence and the use of parameterized policies, we justify statistical consistency and a coverage guarantee on bounding the optimality gap using our approaches. Our developments entail the establishment of several new statistical properties of the so-called multisample <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$U$</tex>-process that closely connect to multistage stochastic optimization.