Moment Relaxations for Data-Driven Wasserstein Distributionally Robust Optimization

TL;DR

This paper introduces moment relaxation techniques for data-driven Wasserstein distributionally robust optimization, ensuring asymptotic consistency and demonstrating their effectiveness through numerical experiments.

Contribution

It develops moment relaxations for Wasserstein DRO problems with conditions for asymptotic consistency, supported by theoretical analysis and numerical validation.

Findings

Relaxations are asymptotically consistent under certain conditions.

Numerical experiments confirm the effectiveness of the proposed relaxations.

Examples illustrate the necessity of the identified conditions.

Abstract

We propose moment relaxations for data-driven Wasserstein distributionally robust optimization problems. Conditions are identified to ensure asymptotic consistency of such relaxations for both single-stage and two-stage problems, together with examples that illustrate their necessity. Numerical experiments are also included to illustrate the proposed relaxations.