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Main Authors: Morinaga, Daiki, Akimoto, Youhei
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2401.14014
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author Morinaga, Daiki
Akimoto, Youhei
author_facet Morinaga, Daiki
Akimoto, Youhei
contents 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.
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institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Theoretical Analysis of Explicit Averaging and Novel Sign Averaging in Comparison-Based Search
Morinaga, Daiki
Akimoto, Youhei
Neural and Evolutionary Computing
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.
title Theoretical Analysis of Explicit Averaging and Novel Sign Averaging in Comparison-Based Search
topic Neural and Evolutionary Computing
url https://arxiv.org/abs/2401.14014