Kriging hyperparameter tuning strategies

Abstract

Response surfaces have been extensively used as a method of building effective surrogate models of high-fidelity
computational simulations. Of the numerous types of response surface models, kriging is perhaps one of the most
effective, due to its ability to model complicated responses through interpolation or regression of known data while
providing an estimate of the error in its prediction. There is, however, little information indicating the extent to which
the hyperparameters of a kriging model need to be tuned for the resulting surrogate model to be effective. The
following paper addresses this issue by investigating how often and how well it is necessary to tune the
hyperparameters of a kriging model as it is updated during an optimization process. To this end, an optimization
benchmarking procedure is introduced and used to assess the performance of five different tuning strategies over a
range of problem sizes. The results of this benchmark demonstrate the performance gains that can be associated with
reducing the complexity of the hyperparameter tuning process for complicated design problems. The strategy of
tuning hyperparameters only once after the initial design of experiments is shown to perform poorly.

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Identifiers

ORCID for David J.J. Toal: orcid.org/0000-0002-2203-0302

ORCID for Andy J. Keane: orcid.org/0000-0001-7993-1569

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