Graceful scaling on uniform versus steep-tailed noise

Abstract

Recently, different evolutionary algorithms (EAs) have been analyzed in noisy environments. The most frequently used noise model for this was additive posterior noise (noise added after the fitness evaluation) taken from a Gaussian distribution. In particular, for this setting it was shown that the (μ + 1)-EA on OneMax does not scale gracefully (higher noise cannot efficiently be compensated by higher μ). In this paper we want to understand whether there is anything special about the Gaussian distribution which makes the (μ + 1)-EA not scale gracefully. We keep the setting of posterior noise, but we look at other distributions. We see that for exponential tails the (μ + 1)-EA on OneMax does also not scale gracefully, for similar reasons as in the case of Gaussian noise. On the other hand, for uniform distributions (as well as other, similar distributions) we see that the (μ + 1)-EA on OneMax does scale gracefully, indicating the importance of the noise model.