  In black-box optimization, noise in the objective function is inevitable.
Noise disrupts the ranking of candidate solutions in comparison-based
optimization, possibly deteriorating the search performance compared with a
noiseless scenario. Explicit averaging takes the sample average of noisy
objective function values and is widely used as a simple and versatile
noise-handling technique. Although it is suitable for various applications, it
is ineffective if the mean is not finite. We theoretically reveal that explicit
averaging has a negative effect on the estimation of ground-truth rankings when
assuming stably distributed noise without a finite mean. Alternatively, sign
averaging is proposed as a simple but robust noise-handling technique. We
theoretically prove that the sign averaging estimates the order of the medians
of the noisy objective function values of a pair of points with arbitrarily
high probability as the number of samples increases. Its advantages over
explicit averaging and its robustness are also confirmed through numerical
experiments.
