Uniform-in-time weak propagation of chaos for consensus-based optimization
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910808598904832 |
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| author | Bayraktar, Erhan Ekren, Ibrahim Zhou, Hongyi |
| author_facet | Bayraktar, Erhan Ekren, Ibrahim Zhou, Hongyi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00582 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniform-in-time weak propagation of chaos for consensus-based optimization Bayraktar, Erhan Ekren, Ibrahim Zhou, Hongyi Optimization and Control Machine Learning Probability 35Q89, 37N40, 93D50, 82C31, 90C26 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. |
| title | Uniform-in-time weak propagation of chaos for consensus-based optimization |
| topic | Optimization and Control Machine Learning Probability 35Q89, 37N40, 93D50, 82C31, 90C26 |
| url | https://arxiv.org/abs/2502.00582 |