Unifying Distributionally Robust Optimization via Optimal Transport Theory
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909969879662592 |
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| author | Blanchet, Jose Kuhn, Daniel Li, Jiajin Taskesen, Bahar |
| author_facet | Blanchet, Jose Kuhn, Daniel Li, Jiajin Taskesen, Bahar |
| contents | In recent years, two prominent paradigms have shaped distributionally robust optimization (DRO), modeling distributional ambiguity through $ϕ$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05414 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Unifying Distributionally Robust Optimization via Optimal Transport Theory Blanchet, Jose Kuhn, Daniel Li, Jiajin Taskesen, Bahar Optimization and Control Machine Learning In recent years, two prominent paradigms have shaped distributionally robust optimization (DRO), modeling distributional ambiguity through $ϕ$-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. |
| title | Unifying Distributionally Robust Optimization via Optimal Transport Theory |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2308.05414 |