On the robustness of median sampling in noisy evolutionary optimization

Abstract

Evolutionary algorithms (EAs) are a sort of nature-inspired metaheuristics, which have wide applications in various practical optimization problems. In these problems, objective evaluations are usually inaccurate, because noise is almost inevitable in real world, and it is a crucial issue to weaken the negative effect caused by noise. Sampling is a popular strategy, which evaluates the objective a couple of times, and employs the mean of these evaluation results as an estimate of the objective value. In this work, we introduce a novel sampling method, median sampling, into EAs, and illustrate its properties and usefulness theoretically by solving OneMax, the problem of maximizing the number of 1s in a bit string. Instead of the mean, median sampling employs the median of the evaluation results as an estimate. Through rigorous theoretical analysis on OneMax under the commonly used onebit noise, we show that median sampling reduces the expected runtime exponentially. Next, through two special noise models, we show that when the 2-quantile of the noisy fitness increases with the true fitness, median sampling can be better than mean sampling; otherwise, it may fail and mean sampling can be better. The results may guide us to employ median sampling properly in practical applications.

Revisiting Implicit and Explicit Averaging for Noisy Optimization

“…There are two other factors that favor explicit averaging and are worth further investigation. First, using the median instead of the mean of independent evaluations can enable explicit averaging to deal with noise models with heavy tails [12], [11], a noise model in which explicit averaging fails if the conventional mean indicator is used [14]. Second, it is not necessary to resample all solutions κ times.…”

“…More importantly, for noise models that do not follow the central limit theorem, e.g., the Cauchy noise, explicit averaging turned out to be detrimental since it increased the noise strength. Considering the findings in [11] and [12], one potential alternative to this challenge is to use the median of the calculated fitness values, instead of the mean.…”

“…The true fitness is estimated using some statistical indicators. The mean of these κ values is a commonly used statistic for this purpose [6], although the median is a more robust statistic, especially when the distribution of the evaluated fitness has a heavy-tail or includes outliers [11], [12]. Given a population size of λ, the required number of function evaluations per iteration is FEpI = κλ.…”

Effect of small accounting class on learning effectiveness: a study among college students

“…Accordingly, the study defines a small class as having less than 27.5 (28) students. Bian et al (2021) demonstrated that median sampling is possibly preferable to mean sampling when the 2quantile of the noisy fitness increases with the genuine fitness, and the findings may serve as a guide for adequately employing the median sample in practical situations. Deviations in the business environment have created a perceived need for more creative individuals in the accounting profession.…”