Two-Stage Distributionally Robust Conic Linear Programming over 1-Wasserstein Balls
Abstract
This paper studies two-stage distributionally robust conic linear programming under constraint uncertainty over type-1 Wasserstein balls. We present optimality conditions for the dual of the worst-case expectation problem, which characterizes worst-case uncertain parameters for its inner maximization problem. This condition offers an alternative proof, a counter-example, and an extension to previous works. Additionally, the condition highlights the potential advantage of a specific distance metric for out-of-sample performance, as exemplified in a numerical study on a facility location problem with demand uncertainty. A cutting-plane-based algorithm and a variety of algorithmic enhancements are proposed with a finite convergence proof under less stringent assumptions.
Keywords
Cite
@article{arxiv.2211.05903,
title = {Two-Stage Distributionally Robust Conic Linear Programming over 1-Wasserstein Balls},
author = {Geunyeong Byeon and Kaiwen Fang and Kibaek Kim},
journal= {arXiv preprint arXiv:2211.05903},
year = {2024}
}