Bidirectional relation between CMA evolution strategies and natural evolution strategies

Authors:
Youhei Akimoto;Yuichi Nagata;Isao Ono;Shigenobu Kobayashi
Affiliations:
Tokyo Institute of Technology, Midori-ku, Yokohama, Japan and Japan Society for the Promotion of Science;Tokyo Institute of Technology, Midori-ku, Yokohama, Japan;Tokyo Institute of Technology, Midori-ku, Yokohama, Japan;Tokyo Institute of Technology, Midori-ku, Yokohama, Japan
Venue:
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Year:
2010

Citing 9
Cited 2

Natural gradient works efficiently in learning

Neural Computation
Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES)

Evolutionary Computation
Completely Derandomized Self-Adaptation in Evolution Strategies

Evolutionary Computation
Natural Actor-Critic

Neurocomputing
Natural conjugate gradient training of multilayer perceptrons

Neurocomputing
Natural Conjugate Gradient in Variational Inference

Neural Information Processing
Natural Conjugate Gradient on Complex Flag Manifolds for Complex Independent Subspace Analysis

ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part I
Efficient covariance matrix update for variable metric evolution strategies

Machine Learning
Efficient natural evolution strategies

Proceedings of the 11th Annual conference on Genetic and evolutionary computation

Analysis of a natural gradient algorithm on monotonic convex-quadratic-composite functions

Proceedings of the 14th annual conference on Genetic and evolutionary computation
Objective improvement in information-geometric optimization

Proceedings of the twelfth workshop on Foundations of genetic algorithms XII

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.