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Analysis of Noisy Evolutionary Optimization When Sampling Fails
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. Previous studies on
sampling are mainly empirical. In this paper, we first investigate the effect
of sample size from a theoretical perspective. By analyzing the (1+1)-EA on the
noisy LeadingOnes problem, we show that as the sample size increases, the
running time can reduce from exponential to polynomial, but then return to
exponential. This suggests that a proper sample size is crucial in practice.
Then, we investigate what strategies can work when sampling with any fixed
sample size fails. By two illustrative examples, we prove that using parent or
offspring populations can be better. Finally, we construct an artificial noisy
example to show that when using neither sampling nor populations is effective,
adaptive sampling (i.e., sampling with an adaptive sample size) can work. This,
for the first time, provides a theoretical support for the use of adaptive
sampling
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