Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Bianchi, Pascal, Dragomir, Radu-Alexandru, Priser, Victor
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7082001167
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