  This paper presents a novel algorithmic study with extensive numerical
experiments of distributionally robust multistage convex optimization (DR-MCO).
Following the previous work on dual dynamic programming (DDP) algorithmic
framework for DR-MCO [48], 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),
risk-neutral and risk-averse multistage stochastic convex optimization (MSCO)
models on multi-commodity 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.
