On the mean-field limit of consensus-based methods
Consensus-based optimization (CBO) employs a swarm of particles evolving as a system of stochastic differential equations (SDEs). Recently, it has been adapted to yield a derivative free sampling method referred to as consensus-based sampling (CBS). In this paper, we investigate the “mean-field limi...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
25 November 2025
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| In: |
Mathematical methods in the applied sciences
Year: 2025, Pages: 1-27 |
| ISSN: | 1099-1476 |
| DOI: | 10.1002/mma.70343 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1002/mma.70343 Verlag, kostenfrei, Volltext: https://onlinelibrary.wiley.com/doi/10.1002/mma.70343 
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| Author Notes: | Marvin Koß, Simon Weissmann, Jakob Zech |
| Summary: | Consensus-based optimization (CBO) employs a swarm of particles evolving as a system of stochastic differential equations (SDEs). Recently, it has been adapted to yield a derivative free sampling method referred to as consensus-based sampling (CBS). In this paper, we investigate the “mean-field limit” of a class of consensus methods, including CBO and CBS. This limit allows to characterize the system's behavior as the number of particles approaches infinity. Building upon prior work that carried out this analysis for other algorithms, we establish the existence of a unique, strong solution for these finite-particle SDEs. We further provide uniform moment estimates, which allow to show a Fokker–Planck equation in the mean-field limit. Finally, we prove that the limiting McKean–Vlasov-type SDE related to the Fokker–Planck equation admits a unique solution. |
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| Item Description: | Zuerst veröffentlicht: 25. November 2025 Gesehen am 23.01.2026 |
| Physical Description: | Online Resource |
| ISSN: | 1099-1476 |
| DOI: | 10.1002/mma.70343 |