On the mean field limit of consensus based methods

Jakob Zech; Marvin Ko{\ss}; Simon Weissmann

On the mean field limit of consensus based methods

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arxiv 2409.03518 v1 pith:QOL3OQBI submitted 2024-09-05 math.OC math.PR

Marvin Ko{ss} , Simon Weissmann , Jakob Zech This is my paper

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keywords consensuslimitequationfieldfokker-planckmeanmethodsparticles

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Consensus based optimization (CBO) employs a swarm of particles evolving as a system of stochastic differential equations (SDEs). Recently, it has been adapted to yield a derivative free sampling method referred to as consensus based sampling (CBS). In this paper, we investigate the ``mean field limit'' of a class of consensus methods, including CBO and CBS. This limit allows to characterize the system's behavior as the number of particles approaches infinity. Building upon prior work such as (Huang and Qiu, 2022), we establish the existence of a unique, strong solution for these finite-particle SDEs. We further provide uniform moment estimates, which allow to show a Fokker-Planck equation in the mean-field limit. Finally, we prove that the limiting McKean-Vlasov type SDE related to the Fokker-Planck equation admits a unique solution.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Mean-Field Model for Two-Layer Neural Networks Trained with Consensus-Based Optimization
cs.LG 2025-11 conditional novelty 5.0 of 10

CBO can train small two-layer networks, a hybrid CBO-Adam method improves convergence and stability, and a Wasserstein mean-field model of CBO has monotonically decreasing variance.

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