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Selection of a covariance function for a Gaussian random field aimed for modeling global optimization problems

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Abstract

Bayesian approach is actively used to develop global optimization algorithms aimed at expensive black box functions. One of the challenges in this approach is the selection of an appropriate model for the objective function. Normally, a Gaussian random field is chosen as a theoretical model. However, the problem of estimation of parameters, using objective function values, is not thoroughly researched. In this paper, we consider the behavior of the maximum likelihood estimators of parameters of the homogeneous isotropic Gaussian random field with squared exponential covariance function. We also compare properties of exponential covariance function models.

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Acknowledgements

The work of A.Zilinskas was supported by the Research Council of Lithuania under Grant No. P-MIP-17-61. The work of A.Zhigljavsky was supported by a grant of Crimtant Holding Limited.

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Authors and Affiliations

  1. Institute of Data Science and Digital Technologies, Vilnius University, Akademijos 4, 08663, Vilnius, Lithuania

    Antanas Žilinskas

  2. School of Mathematics, Cardiff University, Cardiff, CF24 1AG, UK

    Anatoly Zhigljavsky

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  1. Anatoly Zhigljavsky
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  2. Antanas Žilinskas
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Correspondence to Antanas Žilinskas.

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Zhigljavsky, A., Žilinskas, A. Selection of a covariance function for a Gaussian random field aimed for modeling global optimization problems. Optim Lett 13, 249–259 (2019). https://doi.org/10.1007/s11590-018-1372-5

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  • DOI: https://doi.org/10.1007/s11590-018-1372-5

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