AI RESEARCH
From Mean-Field Limits to Semiclassical Concentration: Global Convergence of the Canonical Evolutionary Strategy
arXiv CS.LG
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ArXi:2605.30371v1 Announce Type: cross We address the issue of global convergence in stochastic continuous optimization. For that purpose, we formulate the Canonical Evolutionary Strategy (CES) as a controlled mathematical framework to analyze global convergence in evolutionary algorithms via the semiclassical limit of a Schr{\"o}dinger-type replicator-mutator equation. We provide a rigorous hierarchy from a discrete individual-based dynamics to a deterministic mean-field limit, nstrating that global convergence is governed by the principal eigenfunction of the underlying operator.