Consensus-Based Optimization Beyond Finite-Time Analysis
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911278584299520 |
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| author | Bianchi, Pascal Dragomir, Radu-Alexandru Priser, Victor |
| author_facet | Bianchi, Pascal Dragomir, Radu-Alexandru Priser, Victor |
| contents | We analyze a zeroth-order particle algorithm for the global optimization of a non-convex function, focusing on a variant of Consensus-Based Optimization (CBO) with small but fixed noise intensity. Unlike most previous studies restricted to finite horizons, we investigate its long-time behavior with fixed parameters. In the mean-field limit, a quantitative Laplace principle shows exponential convergence to a neighborhood of the minimizer x * . For finitely many particles, a block-wise analysis yields explicit error bounds: individual particles achieve long-time consistency near x * , and the global best particle converge to x * . The proof technique combines a quantitative Laplace principle with block-wise control of Wasserstein distances, avoiding the exponential blow-up typical of Gr{ö}nwall-based estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Consensus-Based Optimization Beyond Finite-Time Analysis Bianchi, Pascal Dragomir, Radu-Alexandru Priser, Victor Optimization and Control We analyze a zeroth-order particle algorithm for the global optimization of a non-convex function, focusing on a variant of Consensus-Based Optimization (CBO) with small but fixed noise intensity. Unlike most previous studies restricted to finite horizons, we investigate its long-time behavior with fixed parameters. In the mean-field limit, a quantitative Laplace principle shows exponential convergence to a neighborhood of the minimizer x * . For finitely many particles, a block-wise analysis yields explicit error bounds: individual particles achieve long-time consistency near x * , and the global best particle converge to x * . The proof technique combines a quantitative Laplace principle with block-wise control of Wasserstein distances, avoiding the exponential blow-up typical of Gr{ö}nwall-based estimates. |
| title | Consensus-Based Optimization Beyond Finite-Time Analysis |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2509.12907 |