Consensus based optimization via jump-diffusion stochastic differential equations

TL;DR

This paper introduces a novel consensus-based optimization method driven by jump-diffusion stochastic differential equations, demonstrating convergence and improved performance over previous methods through theoretical analysis and numerical experiments.

Contribution

It develops a new jump-diffusion driven CBO method with proven convergence properties and enhanced numerical performance compared to existing approaches.

Findings

Proved convergence of particle system to mean-field limit

Established convergence of discretized system in mean-square sense

Demonstrated improved numerical performance on benchmark functions

Abstract

We introduce a new consensus based optimization (CBO) method where interacting particle system is driven by jump-diffusion stochastic differential equations. We study well-posedness of the particle system as well as of its mean-field limit. The major contributions of this paper are proofs of convergence of the interacting particle system towards the mean-field limit and convergence of a discretized particle system towards the continuous-time dynamics in the mean-square sense. We also prove convergence of the mean-field jump-diffusion SDEs towards global minimizer for a large class of objective functions. We demonstrate improved performance of the proposed CBO method over earlier CBO methods in numerical simulations on benchmark objective functions.