Bidirectional Relation between CMA Evolution Strategies and Natural Evolution Strategies

  • Youhei Akimoto
  • Yuichi Nagata
  • Isao Ono
  • Shigenobu Kobayashi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6238)


This paper investigates the relation between the covariance matrix adaptation evolution strategy and the natural evolution strategy, the latter of which is recently proposed and is formulated as a natural gradient based method on the expected fitness under the mutation distribution. To enable to compare these algorithms, we derive the explicit form of the natural gradient of the expected fitness and transform it into the forms corresponding to the mean vector and the covariance matrix of the mutation distribution. We show that the natural evolution strategy can be viewed as a variant of covariance matrix adaptation evolution strategies using Cholesky update and also that the covariance matrix adaptation evolution strategy can be formulated as a variant of natural evolution strategies.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Youhei Akimoto
    • 1
    • 2
  • Yuichi Nagata
    • 1
  • Isao Ono
    • 1
  • Shigenobu Kobayashi
    • 1
  1. 1.Tokyo Institute of TechnologyYokohamaJapan
  2. 2.Research Fellow of the Japan Society for the Promotion of Science

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