Exponential stability of finite-$N$ consensus-based optimization
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918165733179392 |
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| author | Göttlich, Simone Heieck, Jacob Neuenkirch, Andreas |
| author_facet | Göttlich, Simone Heieck, Jacob Neuenkirch, Andreas |
| contents | We study the finite-agent behavior of Consensus-Based Optimization (CBO), a recent metaheuristic for the global minimization of a function, that combines drift toward a consensus estimate with stochastic exploration. While previous analyses focus on asymptotic mean-field limits, we investigate the stability properties of CBO for finite population size \( N \). Following a hierarchical approach, we first analyze a deterministic formulation of the algorithm and then extend our results to the fully stochastic setting governed by a system of stochastic differential equations. Our analysis reveals that essential stability properties, including almost sure and mean square exponential convergence, persist in both regimes and provides sharp quantitative estimates on the rates of convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19565 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential stability of finite-$N$ consensus-based optimization Göttlich, Simone Heieck, Jacob Neuenkirch, Andreas Optimization and Control We study the finite-agent behavior of Consensus-Based Optimization (CBO), a recent metaheuristic for the global minimization of a function, that combines drift toward a consensus estimate with stochastic exploration. While previous analyses focus on asymptotic mean-field limits, we investigate the stability properties of CBO for finite population size \( N \). Following a hierarchical approach, we first analyze a deterministic formulation of the algorithm and then extend our results to the fully stochastic setting governed by a system of stochastic differential equations. Our analysis reveals that essential stability properties, including almost sure and mean square exponential convergence, persist in both regimes and provides sharp quantitative estimates on the rates of convergence. |
| title | Exponential stability of finite-$N$ consensus-based optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.19565 |