  The aim of black-box optimization is to optimize an objective function within
the constraints of a given evaluation budget. In this problem, it is generally
assumed that the computational cost for evaluating a point is large; thus, it
is important to search efficiently with as low budget as possible. Bayesian
optimization is an efficient method for black-box optimization and provides
exploration-exploitation trade-off by constructing a surrogate model that
considers uncertainty of the objective function. However, because Bayesian
optimization should construct the surrogate model for the entire search space,
it does not exhibit good performance when points are not sampled sufficiently.
In this study, we develop a heuristic method refining the search space for
Bayesian optimization when the available evaluation budget is low. The proposed
method refines a promising region by dividing the original region so that
Bayesian optimization can be executed with the promising region as the initial
search space. We confirm that Bayesian optimization with the proposed method
outperforms Bayesian optimization alone and shows equal or better performance
to two search-space division algorithms through experiments on the benchmark
functions and the hyperparameter optimization of machine learning algorithms.
