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Pré-Publication, Document De Travail Année : 2020

BCMA-ES: a conjugate prior Bayesian optimization view

Rida Laraki
Jamal Atif

Résumé

CMA-ES is one of the state of the art evolutionary optimization methods because of its capacity to adapt covariance to information geometry. It uses prior information to form a best guess about the distribution of the minimum. We show this can be reformulated as a Bayesian optimization problem for the sampling of the optimum. Thanks to Normal Inverse Wishart (NIW) distribution, that is a conjugate prior for the multi variate normal distribution, we can derive a numerically efficient algorithm Bayesian CMA-ES that obtains similar performance as the traditional CMA-ES on multiple benchmarks and provides a new justification for the CMA-ES updates equations. This novel paradigm for Bayesian CMA-ES provides a powerful bridge between evolutionary and Bayesian optimization, showing the profound similarities and connections between these traditionally opposed methods and opening horizon for variations and mix strategies on these methods.
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Dates et versions

hal-02977523 , version 1 (25-10-2020)

Identifiants

  • HAL Id : hal-02977523 , version 1

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Eric Benhamou, David Saltiel, Rida Laraki, Jamal Atif. BCMA-ES: a conjugate prior Bayesian optimization view. 2020. ⟨hal-02977523⟩
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