Abstract
One area where active learning plays an important role is black-box optimization of objective functions with expensive evaluations.
To deal with such evaluations, continuous black-box optimization has adopted an approach called surrogate modelling or metamodelling, which consists in replacing the true black-box objective in some of its evalu- ations with a suitable regression model, the selection of evaluations for replacement being an active learning task. This paper concerns surrogate modelling in the context of a surrogate-assisted variant of the continuous black-box optimizer Covariance Matrix Adaptation Evolution Strategy.
It reports the experimental investigation of surrogate models combining artificial neural networks with Gaussian processes, for which it considers six different covariance functions. The experiments were performed on the set of 24 noiseless benchmark functions of the platform Comparing
Continuous Optimizers COCO with 5 different dimensionalities. Their results revealed that the most suitable covariance function for this com- bined kind of surrogate models is the rational quadratic followed by the
Matérn 25 and squared exponential. Moreover, the rational quadratic and squared exponential covariances were found interchangeable in the sense that for no function, no group of functions, no dimension and combina- tion of them, the performance of the respective surrogate models was significantly different.