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arXiv · 2308.05414

Unifying Distributionally Robust Optimization via Optimal Transport Theory

Jose Blanchet·Daniel Kuhn·Jiajin Li·Bahar Taskesen
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Abstract

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. We further establish key duality results and develop tractable reformulations that highlight the practical power of our unified approach.

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Jose Blanchet, Daniel Kuhn, Jiajin Li, Bahar Taskesen. 2023-08-10. Unifying Distributionally Robust Optimization via Optimal Transport Theory. https://arxiv.org/abs/2308.05414

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