{"ID":2870336,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.12907","arxiv_id":"2509.12907","title":"Consensus-Based Optimization Beyond Finite-Time Analysis","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.","short_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...","url_abs":"https://arxiv.org/abs/2509.12907","url_pdf":"https://arxiv.org/pdf/2509.12907v3","authors":"[\"Pascal Bianchi\",\"Radu-Alexandru Dragomir\",\"Victor Priser\"]","published":"2025-09-16T10:00:53Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}