# On the Robustness of Median Sampling in Noisy Evolutionary Optimization

## TL;DR

This paper introduces median sampling into evolutionary algorithms to improve robustness against noise, demonstrating theoretically that it can exponentially reduce runtime under certain noise conditions, with practical guidance for its application.

## Contribution

The paper presents the novel use of median sampling in EAs, providing theoretical analysis of its advantages and limitations compared to mean sampling under noisy conditions.

## Key findings

- Median sampling reduces expected runtime exponentially under onebit noise.
- Median sampling outperforms mean sampling when the noise's 2-quantile increases with true fitness.
- Median sampling may fail when the noise's 2-quantile does not increase with true fitness.

## 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.