Noisy Optimization: Convergence with a Fixed Number of Resamplings

It is known that evolution strategies in continuous domains might not converge in the presence of noise [3, 14]. It is also known that, under mild assumptions, and using an increasing number of resamplings, one can mitigate the effect of additive noise [4] and recover convergence. We show new sufficient conditions for the convergence of an evolutionary algorithm with constant number of resamplings; in particular, we get fast rates (log-linear convergence) provided that the variance decreases around the optimum slightly faster than in the so-called multiplicative noise model.

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