Noisy optimization convergence rates

Sandra Astete Morales, Jialin Liu, Olivier Teytaud

Abstract: We consider noisy optimization problems, without the assumption of variance vanishing in the neighborhood of the optimum. We show mathematically that evolutionary algorithms with simple rules with exponential number of resamplings lead to a log-log convergence rate (log of the distance to the optimum linear in the log of the number of resamplings), as well as with number of resamplings polynomial in the inverse step-size.