2025/02/01 by Bayraktar, Erhan, Ekren, Ibrahim, Zhou, Hongyi · 1 citation
#35Q89 #37N40 #82C31 #90C26 #93D50 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Probability (math.PR)
paper · doi:10.48550/arxiv.2502.00582
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.