Kriging hyperparameter tuning strategies

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.