Marginal flows of non-entropic weak Schrödinger bridges
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914428510797824 |
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| author | Hernández, Camilo Tangpi, Ludovic |
| author_facet | Hernández, Camilo Tangpi, Ludovic |
| contents | This paper introduces a dynamic formulation of divergence-regularized optimal transport with weak targets on the path space. In our formulation, the classical relative entropy penalty is replaced by a general convex divergence, and terminal constraints are imposed in a weak sense. We establish well-posedness and a convex dual formulation, together with a dual existence result and explicit structural characterizations of primal and dual optimizers. Specifically, the optimal path measure admits an explicit density relative to a reference diffusion, generalizing the classical Schr{ö}dinger system. In the case of zero transport cost, which corresponds to a non-entropic dynamic Schr{ö}dinger problem, we further characterize the flow of time marginals of the optimal bridge, recovering known results in the entropic setting and providing new descriptions for non-entropic divergences, including the $χ^2$-divergence |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21261 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Marginal flows of non-entropic weak Schrödinger bridges Hernández, Camilo Tangpi, Ludovic Probability Optimization and Control This paper introduces a dynamic formulation of divergence-regularized optimal transport with weak targets on the path space. In our formulation, the classical relative entropy penalty is replaced by a general convex divergence, and terminal constraints are imposed in a weak sense. We establish well-posedness and a convex dual formulation, together with a dual existence result and explicit structural characterizations of primal and dual optimizers. Specifically, the optimal path measure admits an explicit density relative to a reference diffusion, generalizing the classical Schr{ö}dinger system. In the case of zero transport cost, which corresponds to a non-entropic dynamic Schr{ö}dinger problem, we further characterize the flow of time marginals of the optimal bridge, recovering known results in the entropic setting and providing new descriptions for non-entropic divergences, including the $χ^2$-divergence |
| title | Marginal flows of non-entropic weak Schrödinger bridges |
| topic | Probability Optimization and Control |
| url | https://arxiv.org/abs/2512.21261 |