Uniform-in-time propagation of chaos for Consensus-Based Optimization
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915804838100992 |
|---|---|
| author | Gerber, Nicolai Hoffmann, Franca Kim, Dohyeon Vaes, Urbain |
| author_facet | Gerber, Nicolai Hoffmann, Franca Kim, Dohyeon Vaes, Urbain |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniform-in-time propagation of chaos for Consensus-Based Optimization Gerber, Nicolai Hoffmann, Franca Kim, Dohyeon Vaes, Urbain Probability Analysis of PDEs Optimization and Control 35Q93, 65C35, 70F45, 35K55 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. |
| title | Uniform-in-time propagation of chaos for Consensus-Based Optimization |
| topic | Probability Analysis of PDEs Optimization and Control 35Q93, 65C35, 70F45, 35K55 |
| url | https://arxiv.org/abs/2505.08669 |