Loss-aware distributionally robust optimization via trainable optimal transport ambiguity sets
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908541139288064 |
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| author | Ohnemus, Jonas Fochesato, Marta Zuliani, Riccardo Lygeros, John |
| author_facet | Ohnemus, Jonas Fochesato, Marta Zuliani, Riccardo Lygeros, John |
| contents | Optimal-Transport Distributionally Robust Optimization (OT-DRO) robustifies data-driven decision-making under uncertainty by capturing the sampling-induced statistical error via optimal transport ambiguity sets. The standard OT-DRO pipeline consists of a two-step procedure, where the ambiguity set is first designed and subsequently embedded into the downstream OT-DRO problem. However, this separation between uncertainty quantification and optimization might result in excessive conservatism. We introduce an end-to-end pipeline to automatically learn decision-focused ambiguity sets for OT-DRO problems, where the loss function informs the shape of the optimal transport ambiguity set, leading to less conservative yet distributionally robust decisions. We formulate the learning problem as a bilevel optimization program and solve it via a hypergradient-based method. By leveraging the recently introduced nonsmooth conservative implicit function theorem, we establish convergence to a critical point of the bilevel problem. We present experiments validating our method on standard portfolio optimization and linear regression tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12689 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Loss-aware distributionally robust optimization via trainable optimal transport ambiguity sets Ohnemus, Jonas Fochesato, Marta Zuliani, Riccardo Lygeros, John Optimization and Control Systems and Control Optimal-Transport Distributionally Robust Optimization (OT-DRO) robustifies data-driven decision-making under uncertainty by capturing the sampling-induced statistical error via optimal transport ambiguity sets. The standard OT-DRO pipeline consists of a two-step procedure, where the ambiguity set is first designed and subsequently embedded into the downstream OT-DRO problem. However, this separation between uncertainty quantification and optimization might result in excessive conservatism. We introduce an end-to-end pipeline to automatically learn decision-focused ambiguity sets for OT-DRO problems, where the loss function informs the shape of the optimal transport ambiguity set, leading to less conservative yet distributionally robust decisions. We formulate the learning problem as a bilevel optimization program and solve it via a hypergradient-based method. By leveraging the recently introduced nonsmooth conservative implicit function theorem, we establish convergence to a critical point of the bilevel problem. We present experiments validating our method on standard portfolio optimization and linear regression tasks. |
| title | Loss-aware distributionally robust optimization via trainable optimal transport ambiguity sets |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2509.12689 |