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

TL;DR

This paper develops a data-driven distributionally robust multistage convex optimization framework using Wasserstein ambiguity sets, providing performance guarantees and efficient algorithms, with empirical results showing advantages over traditional models in small data scenarios.

Contribution

It introduces a novel Wasserstein-based data-driven DR-MCO model with convergence-guaranteed algorithms and out-of-sample performance assurances, extending previous dual dynamic programming approaches.

Findings

DR-MCO models outperform MRCO and MSCO with small data.

The proposed algorithms ensure convergence of DDP in DR-MCO.

Models have adjustable in-sample conservatism and performance guarantees.

Abstract

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, 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.