标题： 基于一致性的优化中时间均匀的弱传播混沌 显示英文标题

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

摘要： 我们研究在有界搜索域上基于共识的优化（CBO）方法的统一时间弱传播混沌。 我们应用了Delarue和Tse（ArXiv:2104.14973）工作中开发的研究相互作用粒子系统长时间行为的方法。 我们的工作表明，弱误差在时间上是均匀的，其阶数为$O(N^{-1})$，其中$N$表示粒子的数量。 证明背后的主要策略是利用线性化福克-普朗克方程对弱误差进行分解，以及它们的Sobolev范数的指数衰减。 因此，我们的结果导致了CBO粒子系统的经验分布，在种群规模和运行时间方面，以Wasserstein型度量收敛到全局最小值处的狄拉克-δ分布。 显示英文摘要

摘要： 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.