Consensus based optimization via jump-diffusion stochastic differential equations

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.

References in corpus (4)

• A consensus-based model for global optimization and its mean-field limit
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• Binary interaction methods for high dimensional global optimization and machine learning
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• Consensus-Based Optimization with Truncated Noise
• A multiscale Consensus-Based algorithm for multi-level optimization
• Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications
• Swarm-based optimization with jumps: a kinetic BGK framework and convergence analysis