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

arXiv: https://arxiv.org/abs/2502.00582 · HTML: https://mlsanity.com/paper/2502.00582/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2025.

## Abstract (arXiv)

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.