Uniform-in-time weak propagation of chaos for consensus-based optimization

• URL: http://arxiv.org/abs/2502.00582v1
• Date: Sat, 01 Feb 2025 22:38:10 GMT
• Title: Uniform-in-time weak propagation of chaos for consensus-based optimization
• Authors: Erhan Bayraktar, Ibrahim Ekren, Hongyi Zhou,
• Abstract summary: We study the uniform-in-time weak propagation of chaos for the consensus-based optimization (CBO) method on a bounded searching domain. Our work shows that the weak error has order $O(N-1)$ uniformly in time, where $N$ denotes the number of particles.
• Score: 4.533408985664949
• License:
• Abstract: We study the uniform-in-time weak propagation of chaos for the consensus-based optimization (CBO) method on a bounded searching domain. We apply the methodology for studying long-time behaviors of interacting particle systems developed in the work of Delarue and Tse (ArXiv:2104.14973). Our work shows that the weak error has order $O(N^{-1})$ uniformly in time, where $N$ denotes the number of particles. The main strategy behind the proofs are the decomposition of the weak errors using the linearized Fokker-Planck equations and the exponential decay of their Sobolev norms. Consequently, our result leads to the joint convergence of the empirical distribution of the CBO particle system to the Dirac-delta distribution at the global minimizer in population size and running time in Wasserstein-type metrics.

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