Analysis of Noisy Evolutionary Optimization When Sampling Fails

TL;DR

This paper investigates the limitations of fixed sample size sampling in noisy evolutionary optimization and demonstrates that adaptive sampling and population strategies can sometimes be more effective, providing theoretical insights into their advantages.

Contribution

It offers the first theoretical analysis showing fixed sample size sampling can fail, and highlights the potential of adaptive sampling and population strategies in noisy optimization.

Findings

Fixed sample size sampling can be ineffective in certain noisy scenarios.

Population-based strategies can outperform sampling in some artificial examples.

Adaptive sampling can succeed where fixed sampling and populations fail.

Abstract

In noisy evolutionary optimization, sampling is a common strategy to deal with noise. By the sampling strategy, the fitness of a solution is evaluated multiple times (called \emph{sample size}) independently, and its true fitness is then approximated by the average of these evaluations. Most previous studies on sampling are empirical, and the few theoretical studies mainly showed the effectiveness of sampling with a sufficiently large sample size. In this paper, we theoretically examine what strategies can work when sampling with any fixed sample size fails. By constructing a family of artificial noisy examples, we prove that sampling is always ineffective, while using parent or offspring populations can be helpful on some examples. We also construct an artificial noisy example to show that when using neither sampling nor populations is effective, a tailored adaptive sampling (i.e., sampling with an adaptive sample size) strategy can work. These findings may enhance our understanding of sampling to some extent, but future work is required to validate them in natural situations.