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Uniform-in-time mean-field limit estimate for the Consensus-Based Optimization
Hui Huang, Hicham Kouhkouh · 2024-11-06 · via math.PR updates on arXiv.org

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 $κ\in (0,1)$. 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.

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