  Building surrogate models is one common approach when we attempt to learn
unknown black-box functions. Bayesian optimization provides a framework which
allows us to build surrogate models based on sequential samples drawn from the
function and find the optimum. Tuning algorithmic parameters to optimize the
performance of large, complicated "black-box" application codes is a specific
important application, which aims at finding the optima of black-box functions.
Within the Bayesian optimization framework, the Gaussian process model produces
smooth or continuous sample paths. However, the black-box function in the
tuning problem is often non-smooth. This difficult tuning problem is worsened
by the fact that we usually have limited sequential samples from the black-box
function. Motivated by these issues encountered in tuning, we propose a novel
additive Gaussian process model called clustered Gaussian process (cGP), where
the additive components are induced by clustering. In the examples we studied,
the performance can be improved by as much as 90% among repetitive experiments.
By using this surrogate model, we want to capture the non-smoothness of the
black-box function. In addition to an algorithm for constructing this model, we
also apply the model to several artificial and real applications to evaluate
it.
