A general perspective on CBO methods with stochastic rate of information
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913961898672128 |
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| author | Almi, Stefano Baldi, Alessandro Morandotti, Marco Solombrino, Francesco |
| author_facet | Almi, Stefano Baldi, Alessandro Morandotti, Marco Solombrino, Francesco |
| contents | This paper studies a class of Consensus-Based Optimization (CBO) models featuring an additional stochastic rate of information, modeling the agents' knowledge of the environment and energy landscape. The well-posedness of the stochastic system is proved, together with its finite-particle approximation and the mean-field convergence to a kinetic PDE. Particles are shown to concentrate around the consensus point under mild assumptions on the initial spatial distribution and initial level of knowledge. In particular, the analysis unveils that a positive, however small, initial level of knowledge is enough for convergence to consensus to happen. The framework presented is general enough to include the first instances of CBO proposed in the literature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_20029 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A general perspective on CBO methods with stochastic rate of information Almi, Stefano Baldi, Alessandro Morandotti, Marco Solombrino, Francesco Optimization and Control Analysis of PDEs 34F05, 60K35, 93A16, 60H10, 90C56, 35Q84 This paper studies a class of Consensus-Based Optimization (CBO) models featuring an additional stochastic rate of information, modeling the agents' knowledge of the environment and energy landscape. The well-posedness of the stochastic system is proved, together with its finite-particle approximation and the mean-field convergence to a kinetic PDE. Particles are shown to concentrate around the consensus point under mild assumptions on the initial spatial distribution and initial level of knowledge. In particular, the analysis unveils that a positive, however small, initial level of knowledge is enough for convergence to consensus to happen. The framework presented is general enough to include the first instances of CBO proposed in the literature. |
| title | A general perspective on CBO methods with stochastic rate of information |
| topic | Optimization and Control Analysis of PDEs 34F05, 60K35, 93A16, 60H10, 90C56, 35Q84 |
| url | https://arxiv.org/abs/2507.20029 |