A modified Consensus-Based Optimization model: consensus formation and uniform-in-time propagation of chaos
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914168870797312 |
|---|---|
| author | Choi, Young-Pil Lee, Seungchan Song, Sihyun |
| author_facet | Choi, Young-Pil Lee, Seungchan Song, Sihyun |
| contents | We introduce a modified Consensus-Based Optimization model that admits a fully unified and rigorous analysis of its finite-particle dynamics, the associated McKean--Vlasov equation, and their optimization behavior under a single set of structural framework. The key ingredient is a regularized Gibbs weight that stabilizes the consensus point and avoids degeneracies present in the classical formulation, eliminating the need for cutoffs, rescaling, or boundedness assumptions on the objective function. Our first main result establishes large-time consensus for the particle system: when the drift exceeds an explicit threshold, all particles converge exponentially to a common random limit that concentrates near the global minimizer. Our second result proves uniform-in-time propagation of chaos, providing quantitative and dimension-free convergence of the empirical measure to the McKean--Vlasov dynamics. Finally, we show that the mean-field system reaches deterministic consensus and that its consensus point approaches the global minimizer in the regime of highly concentrated Gibbs weights. Together, these results yield a unified and internally consistent theoretical framework for consensus-based optimization under substantially relaxed regularity assumptions on the objective function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19116 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A modified Consensus-Based Optimization model: consensus formation and uniform-in-time propagation of chaos Choi, Young-Pil Lee, Seungchan Song, Sihyun Probability Analysis of PDEs Optimization and Control 35Q93, 70F10, 35B40, 37N40 We introduce a modified Consensus-Based Optimization model that admits a fully unified and rigorous analysis of its finite-particle dynamics, the associated McKean--Vlasov equation, and their optimization behavior under a single set of structural framework. The key ingredient is a regularized Gibbs weight that stabilizes the consensus point and avoids degeneracies present in the classical formulation, eliminating the need for cutoffs, rescaling, or boundedness assumptions on the objective function. Our first main result establishes large-time consensus for the particle system: when the drift exceeds an explicit threshold, all particles converge exponentially to a common random limit that concentrates near the global minimizer. Our second result proves uniform-in-time propagation of chaos, providing quantitative and dimension-free convergence of the empirical measure to the McKean--Vlasov dynamics. Finally, we show that the mean-field system reaches deterministic consensus and that its consensus point approaches the global minimizer in the regime of highly concentrated Gibbs weights. Together, these results yield a unified and internally consistent theoretical framework for consensus-based optimization under substantially relaxed regularity assumptions on the objective function. |
| title | A modified Consensus-Based Optimization model: consensus formation and uniform-in-time propagation of chaos |
| topic | Probability Analysis of PDEs Optimization and Control 35Q93, 70F10, 35B40, 37N40 |
| url | https://arxiv.org/abs/2511.19116 |