A Generalized Sinkhorn Algorithm for Mean-Field Schr\"odinger Bridge
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.
Cite
@article{arxiv.2604.06531,
title = {A Generalized Sinkhorn Algorithm for Mean-Field Schr\"odinger Bridge},
author = {Asmaa Eldesoukey and Yongxin Chen and Abhishek Halder},
journal= {arXiv preprint arXiv:2604.06531},
year = {2026}
}