Fast and robust consensus-based optimization via optimal feedback control
File(s)
Preprint version
OA Location
Author(s)
Huang, Yuyang
Herty, Michael
Kalise, Dante
Kantas, Nikolas
Type
preprint
Abstract
We propose a variant of consensus-based optimization (CBO) algorithms, controlled-CBO, which introduces a feedback control term to improve convergence towards global minimizers of non-convex functions in multiple dimensions. The feedback law is a gradient of a numerical approximation to the Hamilton-Jacobi-Bellman (HJB) equation, which serves as a proxy of the original objective function. Thus, the associated control signal furnishes gradient-like information to facilitate the identification of the global minimum without requiring derivative computation from the objective function itself. The proposed method exhibits significantly improved performance over standard CBO methods in numerical experiments, particularly in scenarios involving a limited number of particles, or where the initial particle ensemble is not well positioned with respect to the global minimum. At the same time, the modification keeps the algorithm amenable to theoretical analysis in the mean-field sense. The superior convergence rates are assessed experimentally.
Date Issued
2025-07-27
Citation
arXiv, 2025
Journal / Book Title
arXiv
Copyright Statement
Copyright © 2025 The Authors. This work is licensed under a Creative Commons Attribution 4.0 International License.
License URL
Description
Preprint version
Subjects
global optimization
consensus-based optimization
Hamilton-Jacobi-Bellman PDEs
high-dimensional polynomial approximation MSC codes. 65K10
35Q93
90C56