A detailed analysis of kernel parameters in Gaussian process-based optimization

The global optimization of expensive-to-evaluate functions frequently occurs in many real-world applications. Among the methods developed for solving such problems, Efficient Global Optimization (EGO) is regarded as one of the state-of-the-art unconstrained continuous optimization algorithms. The most important control on the efficiency of EGO is the Gaussian process covariance function which must be chosen together with the objective function. Traditionally, a param-eterized family of covariance functions is considered whose parameters are learned by maximum likelihood or cross-validation. In this paper, we theoretically and empirically analyze the effect of length-scale covariance parameters and nugget on the design of experiments generated by EGO and the associated optimization performance