Mean-field limits for Consensus-Based Optimization and Sampling
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For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transpose convergence results obtained at the mean-field level to the finite ensemble size setting, it is desirable to obtain estimates on the distance, in an appropriate metric, between the particle dynamics and the corresponding mean-field dynamics. In this talk, we present quantitative mean-field limit results for two related interacting particle systems: Consensus-Based Optimization and Consensus-Based Sampling. Our approach extends Sznitman's classical argument: in order to circumvent issues related to the lack of global Lipschitz continuity of the coefficients, we discard an event of small probability, the contribution of which is controlled using moment estimates for the particle systems.
