# Uniform-in-time propagation of chaos for Consensus-Based Optimization

arXiv: https://arxiv.org/abs/2505.08669 · HTML: https://mlsanity.com/paper/2505.08669/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 May 2025.

## Built on by (most cited first, 1 of 1)

- [Mean-Field Model for Two-Layer Neural Networks Trained with Consensus-Based Optimization](https://mlsanity.com/paper/2511.21466/) (2025)

## Abstract (arXiv)

We study the derivative-free global optimization algorithm Consensus-Based Optimization (CBO), establishing uniform-in-time propagation of chaos as well as an almost uniform-in-time stability result for the microscopic particle system. Moreover, we prove almost sure exponential convergence of the microscopic CBO system around a point close to the global minimizer. The proof of these results is based on a novel stability estimate for the weighted mean and on a quantitative concentration inequality for the microscopic particle system around the empirical mean. Our propagation of chaos result recovers the classical Monte Carlo rate, with a prefactor that depends explicitly on the parameters of the problem. Notably, in the case of CBO with anisotropic noise, this prefactor is independent of the problem dimension.