aiqbench analysis
This paper introduces a generalized Sinkhorn algorithm to solve the nonconvex mean-field Schrödinger bridge problem for large-scale multi-agent systems. By extending the Hopf-Cole transform, it provides convergence guarantees and numerical solutions for guiding interacting diffusion processes under specific deadlines. The work advances theoretical optimization methods applicable to complex control problems in machine learning and robotics.
A Generalized Sinkhorn Algorithm for Mean-Field Schr\"odinger Bridge
arXiv:2604.06531v3 Announce Type: replace-cross 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.
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.
Optimization and Control (math.OC); Machine Learning (cs.LG); Multiagent Systems (cs.MA); Systems and Control (eess.SY); Machine Learning (stat.ML)
arXiv:2604.06531 [math.OC]
(or arXiv:2604.06531v3 [math.OC] for this version)
Full text under the publisher's open licence · 155 words
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