Two-Stage Distributionally Robust Optimization: Intuitive Understanding and Algorithm Development from the Primal Perspective

TL;DR

This paper offers a primal perspective on two-stage distributionally robust optimization, leading to a new, efficient decomposition algorithm that outperforms existing methods in solving complex facility location problems.

Contribution

It introduces a novel primal approach to DRO, enabling the development of a fast, general decomposition algorithm with theoretical guarantees and practical efficiency.

Findings

Algorithm significantly outperforms existing methods in speed.

Successfully solves previously intractable practical instances.

Provides theoretical analysis of convergence and complexity.

Abstract

In this paper, we study the two-stage distributionally robust optimization (DRO) problem from the primal perspective. Unlike existing approaches, this perspective allows us to build a deeper and more intuitive understanding on DRO, to leverage classical and well-established solution methods and to develop a general and fast decomposition algorithm (and its variants), and to address a couple of unsolved issues that are critical for modeling and computation. Theoretical analyses regarding the strength, convergence, and iteration complexity of the developed algorithm are also presented. A numerical study on different types of instances of the distributionally robust facility location problem demonstrates that the proposed solution algorithm (and its variants) significantly outperforms existing methods. It solves instances up to several orders of magnitude faster, and successfully addresses new types of practical instances that previously could not be handled. We believe these results will significantly enhance the accessibility of DRO, break down barriers, and unleash its potential to solve real world challenges.