Bidirectional Relation between CMA Evolution Strategies and Natural Evolution Strategies
Bidirectional Relation between CMA Evolution Strategies and Natural Evolution Strategies
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DOI：
10.1007/978-3-642-15844-5_16
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发表时间：
2010-09
期刊：
影响因子：
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通讯作者：
Youhei Akimoto;Y. Nagata;I. Ono;S. Kobayashi
中科院分区：
文献类型：
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作者：
Youhei Akimoto;Y. Nagata;I. Ono;S. Kobayashi
本文研究了协方差矩阵适应进化策略和自然进化策略之间的关系，后者是最近提出的，并被制定为基于突变分布下的期望适应度的自然梯度方法。为了能够比较这些算法，我们推导了预期适应度的自然梯度的显式形式，并将其转换为与突变分布的均值向量和协方差矩阵相对应的形式。我们证明，自然进化策略可以被视为使用 Cholesky 更新的协方差矩阵适应进化策略的变体，并且协方差矩阵适应进化策略可以被表述为自然进化策略的变体。
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.