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Sparse Inverse Covariance Learning for CMA-ES with Graphical Lasso

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Anne Auger
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Nikolaus Hansen

Abstract

This paper introduces a variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), denoted as gl-CMA-ES, that utilizes the Graphical Lasso regularization. Our goal is to efficiently solve partially separable optimization problems of a certain class by performing stochastic search with a search model parameterized by a sparse precision , i.e. inverse covariance matrix. We illustrate the effect of the global weight of the l1 regularizer and investigate how Graphical Lasso with non equal weights can be combined with CMA-ES, allowing to learn the conditional dependency structure of problems with sparse Hessian matrices. For non-separable sparse problems, the proposed method with appropriately selected weights, outperforms CMA-ES and improves its scaling, while for dense problems it maintains the same performance.
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Dates and versions

hal-02960269 , version 1 (07-10-2020)
hal-02960269 , version 2 (23-01-2021)

Identifiers

  • HAL Id : hal-02960269 , version 2

Cite

Konstantinos Varelas, Anne Auger, Nikolaus Hansen. Sparse Inverse Covariance Learning for CMA-ES with Graphical Lasso. PPSN 2020 - Sixteenth International Conference on Parallel Problem Solving from Nature, Sep 2020, Leiden, Netherlands. ⟨hal-02960269v2⟩
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