Comparative Analysis of Two-Stage Distributionally Robust Optimization over 1-Wasserstein and 2-Wasserstein Balls
Optimization and Control
2025-01-13 v1
Abstract
This paper investigates advantages of using 2-Wasserstein ambiguity sets over 1-Wasserstein sets in two-stage distributionally robust optimization with right-hand side uncertainty. We examine the worst-case distributions within 1- and 2-Wasserstein balls under both unrestricted and nonnegative orthant supports, highlighting a pathological behavior arising in 1-Wasserstein balls. Closed-form solutions for a single-scenario newsvendor problem illustrate that 2-Wasserstein balls enable more informed decisions. Additionally, a penalty-based dual interpretation suggests that 2-Wasserstein balls may outperform 1-Wasserstein balls across a broader range of Wasserstein radii, even with general support sets.
Keywords
Cite
@article{arxiv.2501.05619,
title = {Comparative Analysis of Two-Stage Distributionally Robust Optimization over 1-Wasserstein and 2-Wasserstein Balls},
author = {Geunyeong Byeon},
journal= {arXiv preprint arXiv:2501.05619},
year = {2025}
}