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Hauptverfasser: Dinu, Catalin-Viorel, Patel, Yash J., Bonet-Monroig, Xavier, Wang, Hao
Format: Preprint
Veröffentlicht: 2024
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Online-Zugang:https://arxiv.org/abs/2409.16757
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author Dinu, Catalin-Viorel
Patel, Yash J.
Bonet-Monroig, Xavier
Wang, Hao
author_facet Dinu, Catalin-Viorel
Patel, Yash J.
Bonet-Monroig, Xavier
Wang, Hao
contents The Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) is one of the most advanced algorithms in numerical black-box optimization. For noisy objective functions, several approaches were proposed to mitigate the noise, e.g., re-evaluations of the same solution or adapting the population size. In this paper, we devise a novel method to adaptively choose the optimal re-evaluation number for function values corrupted by additive Gaussian white noise. We derive a theoretical lower bound of the expected improvement achieved in one iteration of CMA-ES, given an estimation of the noise level and the Lipschitz constant of the function's gradient. Solving for the maximum of the lower bound, we obtain a simple expression of the optimal re-evaluation number. We experimentally compare our method to the state-of-the-art noise-handling methods for CMA-ES on a set of artificial test functions across various noise levels, optimization budgets, and dimensionality. Our method demonstrates significant advantages in terms of the probability of hitting near-optimal function values.
format Preprint
id arxiv_https___arxiv_org_abs_2409_16757
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle An Adaptive Re-evaluation Method for Evolution Strategy under Additive Noise
Dinu, Catalin-Viorel
Patel, Yash J.
Bonet-Monroig, Xavier
Wang, Hao
Neural and Evolutionary Computing
The Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) is one of the most advanced algorithms in numerical black-box optimization. For noisy objective functions, several approaches were proposed to mitigate the noise, e.g., re-evaluations of the same solution or adapting the population size. In this paper, we devise a novel method to adaptively choose the optimal re-evaluation number for function values corrupted by additive Gaussian white noise. We derive a theoretical lower bound of the expected improvement achieved in one iteration of CMA-ES, given an estimation of the noise level and the Lipschitz constant of the function's gradient. Solving for the maximum of the lower bound, we obtain a simple expression of the optimal re-evaluation number. We experimentally compare our method to the state-of-the-art noise-handling methods for CMA-ES on a set of artificial test functions across various noise levels, optimization budgets, and dimensionality. Our method demonstrates significant advantages in terms of the probability of hitting near-optimal function values.
title An Adaptive Re-evaluation Method for Evolution Strategy under Additive Noise
topic Neural and Evolutionary Computing
url https://arxiv.org/abs/2409.16757