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Uniform-in-time mean-field limit estimate for the Consensus-Based Optimization
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abstract
We establish a uniform-in-time estimate for the mean-field convergence of the Consensus-Based Optimization (CBO) algorithm by rescaling the consensus point in the dynamics with a small parameter $\kappa \in (0,1)$. This uniform-in-time estimate is essential, as CBO convergence relies on a sufficiently large time horizon and is crucial for ensuring stable, reliable long-term convergence, the latter being key to the practical effectiveness of CBO methods.
Forward citations
Cited by 3 Pith papers
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CB$^2$O: Consensus-Based Bi-Level Optimization
CB2O is a consensus-based optimization method with a quantile selection step that provably converges to the upper-level minimizer among the lower-level minimizers in the mean-field limit.
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Self-interacting CBO: Existence, uniqueness, and long-time convergence
A self-interacting single-particle CBO process is shown to have its occupation measure converge polynomially to a unique invariant measure; the global-minimizer approximation remains unproven.
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Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games
This paper establishes existence, uniqueness, and a finite-particle mean-field error rate of order N^{-γ} for a multi-species consensus-based algorithm for multiplayer Nash games.
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