Abstract
According to a theorem by Astete-Morales, Cauwet, and Teytaud, “simple Evolution Strategies (ES)” that optimize quadratic functions disturbed by additive Gaussian noise of constant variance can only reach a simple regret log-log convergence slope \(\ge -1/2\) (lower bound). In this paper a population size controlled ES is presented that is able to perform better than the \(-1/2\) limit. It is shown experimentally that the pcCMSA-ES is able to reach a slope of \(-1\) being the theoretical lower bound of all comparison-based direct search algorithms.
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Acknowledgements
This work was supported by the Austrian Science Fund FWF under grant P22649-N23 and by the Austrian funding program COMET (COMpetence centers for Excellent Technologies) in the K-Project Advanced Engineering Design Automation (AEDA).
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Hellwig, M., Beyer, HG. (2016). Evolution Under Strong Noise: A Self-Adaptive Evolution Strategy Can Reach the Lower Performance Bound - The pcCMSA-ES. In: Handl, J., Hart, E., Lewis, P., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds) Parallel Problem Solving from Nature – PPSN XIV. PPSN 2016. Lecture Notes in Computer Science(), vol 9921. Springer, Cham. https://doi.org/10.1007/978-3-319-45823-6_3
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DOI: https://doi.org/10.1007/978-3-319-45823-6_3
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