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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2605.11944 |
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| _version_ | 1866917484892782592 |
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| author | Debouchage, Antoine Wang, Xiaozhen Ren, Zhenjie Buet-Golfouse, Francois |
| author_facet | Debouchage, Antoine Wang, Xiaozhen Ren, Zhenjie Buet-Golfouse, Francois |
| contents | This paper addresses the practical challenge in Entropic Optimal Transport (EOT) where the underlying ground cost function is typically latent and unobserved. Rather than assuming a fixed geometric cost, we adopt a data-driven approach where a shared cost is revealed only through samples from a reference optimal coupling. The question is then: given samples from a reference optimal coupling, can we recover the optimal coupling for new marginals under the same latent cost? We introduce a generative transfer framework that recovers the optimal coupling for new marginals by utilizing an iterative path-wise tilting algorithm. Unlike static importance reweighting, this method evolves the coupling jointly with a marginal transport path, allowing mass to move beyond the reference support. We derive sample-level learning rules for these infinitesimal updates, which yield covariance-type evolution equations for the associated transport vector fields. By integrating this dynamics with Conditional Flow Matching (CFM), we produce a practical sampler for paired data. Finally, we provide theoretical guarantees establishing a global convergence rate of \mathcal{O}(δ), ensuring the generated coupling converges to the target EOT plan in W_1 distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11944 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generative Transfer for Entropic Optimal Transport with Unknown Costs Debouchage, Antoine Wang, Xiaozhen Ren, Zhenjie Buet-Golfouse, Francois Optimization and Control This paper addresses the practical challenge in Entropic Optimal Transport (EOT) where the underlying ground cost function is typically latent and unobserved. Rather than assuming a fixed geometric cost, we adopt a data-driven approach where a shared cost is revealed only through samples from a reference optimal coupling. The question is then: given samples from a reference optimal coupling, can we recover the optimal coupling for new marginals under the same latent cost? We introduce a generative transfer framework that recovers the optimal coupling for new marginals by utilizing an iterative path-wise tilting algorithm. Unlike static importance reweighting, this method evolves the coupling jointly with a marginal transport path, allowing mass to move beyond the reference support. We derive sample-level learning rules for these infinitesimal updates, which yield covariance-type evolution equations for the associated transport vector fields. By integrating this dynamics with Conditional Flow Matching (CFM), we produce a practical sampler for paired data. Finally, we provide theoretical guarantees establishing a global convergence rate of \mathcal{O}(δ), ensuring the generated coupling converges to the target EOT plan in W_1 distance. |
| title | Generative Transfer for Entropic Optimal Transport with Unknown Costs |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.11944 |