A Generalized Sinkhorn Algorithm for Mean-Field Schrödinger Bridge

• URL: http://arxiv.org/abs/2604.06531v2
• Date: Thu, 09 Apr 2026 16:35:00 GMT
• Title: A Generalized Sinkhorn Algorithm for Mean-Field Schrödinger Bridge
• Abstract summary: The mean-field Schrdinger bridge (MFSB) problem concerns designing a minimum-effort controller that guides a diffusion process with nonlocal interaction to reach a given distribution by a fixed deadline.<n>Unlike Schrdinger bridge, the dynamical constraint for MFSB is a population of interacting agents with repulsive controls.<n>We propose a generalization the Hopf-Cole algorithm for MFSB and, on building it, design a Sinkhorn-type algorithm to solve the associated system integro-PDEs.
• Score: 19.922542189921447
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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