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arXiv · 2604.06531

A Generalized Sinkhorn Algorithm for Mean-Field Schr\"odinger Bridge

Asmaa Eldesoukey·Yongxin Chen·Abhishek Halder
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Abstract

The mean-field Schr\"odinger 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 Schr\"odinger 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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Asmaa Eldesoukey, Yongxin Chen, Abhishek Halder. 2026-04-08. A Generalized Sinkhorn Algorithm for Mean-Field Schr\"odinger Bridge. https://arxiv.org/abs/2604.06531

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