The Canonical Evolutionary Strategy converges globally by spectral concentration on the principal eigenfunction of a replicator-mutator operator, explaining survival of the flattest.
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ZOPPA at fixed positive temperature converges under minimal assumptions by acting as an exact proximal point method on a smoothed objective, with explicit connections back to the original function and convergence for its sampled version.
A stochastic particle system is proposed in Hilbert spaces with associated mean-field limit, establishing well-posedness, consensus analysis, and convergence to the minimizer under suitable assumptions on the objective, plus a finite-particle algorithm.
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Convergence of zeroth-order proximal point algorithms in the high-temperature regime
ZOPPA at fixed positive temperature converges under minimal assumptions by acting as an exact proximal point method on a smoothed objective, with explicit connections back to the original function and convergence for its sampled version.
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A derivative-free particle method for optimization in Hilbert spaces
A stochastic particle system is proposed in Hilbert spaces with associated mean-field limit, establishing well-posedness, consensus analysis, and convergence to the minimizer under suitable assumptions on the objective, plus a finite-particle algorithm.