Consensus-based optimization via jump-diffusion stochastic differential equations

Kalise, Dante; Sharma, Akash; Tretyakov, Michael V.

Abstract

We introduce a new consensus-based optimization (CBO) method where an interacting particle system is driven by jump-diffusion stochastic differential equations (SDEs). 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.

Citation

Kalise, D., Sharma, A., & Tretyakov, M. V. (2023). Consensus-based optimization via jump-diffusion stochastic differential equations. Mathematical Models and Methods in Applied Sciences, 33(02), 289-339. https://doi.org/10.1142/S0218202523500082

• Journal Article Type: Article
• Acceptance Date: Dec 14, 2022
• Online Publication Date: Feb 17, 2023
• Publication Date: 2023-02
• Deposit Date: Dec 19, 2022
• Publicly Available Date: Jul 28, 2023
• Journal: Mathematical Models and Methods in Applied Sciences
• Electronic ISSN: 0218-2025
• Publisher: World Scientific
• Peer Reviewed: Peer Reviewed
• Volume: 33
• Issue: 02
• Pages: 289-339
• DOI: https://doi.org/10.1142/S0218202523500082
• Keywords: global non-convex optimization, interacting particle systems, mean-field jump-diffusion SDEs, McKean-Vlasov SDEs with jumps
• Public URL: https://nottingham-repository.worktribe.com/output/15159161
• Publisher URL: https://www.worldscientific.com/doi/10.1142/S0218202523500082
• Additional Information: Electronic version of an article published as Mathematical Models and Methods in Applied Sciences, 33, 02, 2023, 289-339 10.1142/s0218202523500082