Unifying Distributionally Robust Optimization via Optimal Transport Theory

Understand

In recent years, two prominent paradigms have shaped distributionally robust optimization (DRO), modeling distributional ambiguity through $\phi$-divergences and Wasserstein distances, respectively.

• While the former focuses on ambiguity in likelihood ratios, the latter emphasizes ambiguity in outcomes and uses a transportation cost function to capture geometric structure in the outcome space.
• This paper proposes a unified framework that bridges these approaches by leveraging optimal transport (OT) with conditional moment constraints.
• Our formulation enables adversarial distributions to jointly perturb likelihood ratios and outcomes, yielding a generalized OT coupling between the nominal and perturbed distributions.