On Distributionally Robust Multistage Convex Optimization: Data-Driven Models and Performance

This paper presents a novel algorithmic study with extensive numerical experiments of distributionally robust multistage convex optimization (DR-MCO). Following the previous work on the dual dynamic programming (DDP) algorithmic framework for DR-MCO by the same authors, we focus on data-driven DR-MCO models with Wasserstein ambiguity sets that allow probability measures with infinite supports. These data-driven Wasserstein DR-MCO models have out-of-sample performance guarantees and adjustable in-sample conservatism. Then, by exploiting additional concavity or convexity in the uncertain cost functions, we design exact single-stage subproblem oracle (SSSO) implementations that ensure the convergence of DDP algorithms. We test the data-driven Wasserstein DR-MCO models against multistage robust convex optimization (MRCO) and risk-neutral and risk-averse multistage stochastic convex optimization (MSCO) models on multicommodity inventory problems and hydro-thermal power planning problems. The results show that our DR-MCO models could outperform MRCO and MSCO models when the data size is small. Funding: This research was supported mainly by NSF Grant 2316675. The first author was also supported by NSF Grant DMS-1929284 while he was in residence at the Institute for Computational and Experimental Research in Mathematics, Providence, RI. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoo.2024.0049 .