Diagonal Acceleration for Covariance Matrix Adaptation Evolution Strategies

Abstract : We introduce an acceleration for covariance matrix adaptation evolution strategies (CMA-ES) by means of adaptive diagonal decoding (dd-CMA). This diagonal acceleration endows the default CMA-ES with the advantages of separable CMA-ES without inheriting its drawbacks. Technically, we introduce a diagonal matrix D that expresses coordinate-wise variances of the sampling distribution in DCD form. The diagonal matrix can learn a rescaling of the problem in the coordinates within linear number of function evaluations. Diagonal decoding can also exploit separability of the problem, but, crucially, does not compromise the performance on non-separable problems. The latter is accomplished by modulating the learning rate for the diagonal matrix based on the condition number of the underlying correlation matrix. dd-CMA-ES not only combines the advantages of default and separable CMA-ES, but also improves the performance, and even the scaling, of CMA-ES on classes of non-separable test functions that reflect, arguably, a landscape feature commonly observed in practice. The paper makes two further secondary contributions: we introduce two different approaches to guaranty positive definiteness of the covariance matrix with active CMA, which is valuable in particular with large population size; we revise the default parameter setting in CMA-ES, proposing accelerated settings in particular for large dimension. All our contributions can be viewed as independent improvements of CMA-ES, yet they are also complementary and can be seamlessly combined. In numerical experiments with dd-CMA-ES up to dimension 5120, we observe remarkable improvements over the original covariance matrix adaptation on functions with coordinate-wise ill-conditioning. The improvement is observed also for large population sizes up to about dimension squared.
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https://hal.inria.fr/hal-01995373
Contributor : Nikolaus Hansen <>
Submitted on : Saturday, January 26, 2019 - 4:04:02 PM
Last modification on : Monday, May 6, 2019 - 3:39:59 PM
Long-term archiving on : Saturday, April 27, 2019 - 12:52:02 PM

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  • HAL Id : hal-01995373, version 1

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Youhei Akimoto, Nikolaus Hansen. Diagonal Acceleration for Covariance Matrix Adaptation Evolution Strategies. 2019. ⟨hal-01995373⟩

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