A Generalized Sinkhorn Algorithm for Mean-Field Schrödinger Bridge
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908949706440704 |
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| author | Eldesoukey, Asmaa Chen, Yongxin Halder, Abhishek |
| author_facet | Eldesoukey, Asmaa Chen, Yongxin Halder, Abhishek |
| contents | The mean-field Schrödinger bridge (MFSB) problem concerns designing a minimum-effort controller that guides a diffusion process with nonlocal interaction to reach a given distribution from another by a fixed deadline. Unlike the standard Schrödinger bridge, the dynamical constraint for MFSB is the mean-field limit of a population of interacting agents with controls. It serves as a natural model for large-scale multi-agent systems. The MFSB is computationally challenging because the nonlocal interaction makes the problem nonconvex. We propose a generalization of the Hopf-Cole transform for MFSB and, building on it, design a Sinkhorn-type recursive algorithm to solve the associated system of integro-PDEs. Under mild assumptions on the interaction potential, we discuss convergence guarantees for the proposed algorithm. We present numerical examples with repulsive and attractive interactions to illustrate the theoretical contributions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_06531 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Generalized Sinkhorn Algorithm for Mean-Field Schrödinger Bridge Eldesoukey, Asmaa Chen, Yongxin Halder, Abhishek Optimization and Control Machine Learning Multiagent Systems Systems and Control The mean-field Schrödinger bridge (MFSB) problem concerns designing a minimum-effort controller that guides a diffusion process with nonlocal interaction to reach a given distribution from another by a fixed deadline. Unlike the standard Schrödinger bridge, the dynamical constraint for MFSB is the mean-field limit of a population of interacting agents with controls. It serves as a natural model for large-scale multi-agent systems. The MFSB is computationally challenging because the nonlocal interaction makes the problem nonconvex. We propose a generalization of the Hopf-Cole transform for MFSB and, building on it, design a Sinkhorn-type recursive algorithm to solve the associated system of integro-PDEs. Under mild assumptions on the interaction potential, we discuss convergence guarantees for the proposed algorithm. We present numerical examples with repulsive and attractive interactions to illustrate the theoretical contributions. |
| title | A Generalized Sinkhorn Algorithm for Mean-Field Schrödinger Bridge |
| topic | Optimization and Control Machine Learning Multiagent Systems Systems and Control |
| url | https://arxiv.org/abs/2604.06531 |