  Bayesian optimization has attracted huge attention from diverse research
areas in science and engineering, since it is capable of finding a global
optimum of an expensive-to-evaluate black-box function efficiently. In general,
a probabilistic regression model, e.g., Gaussian processes and Bayesian neural
networks, is widely used as a surrogate function to model an explicit
distribution over function evaluations given an input to estimate and a
training dataset. Beyond the probabilistic regression-based Bayesian
optimization, density ratio estimation-based Bayesian optimization has been
suggested in order to estimate a density ratio of the groups relatively close
and relatively far to a global optimum. Developing this line of research
further, a supervised classifier can be employed to estimate a class
probability for the two groups instead of a density ratio. However, the
supervised classifiers used in this strategy are prone to be overconfident for
a global solution candidate. To solve this problem, we propose density ratio
estimation-based Bayesian optimization with semi-supervised learning. Finally,
we demonstrate the experimental results of our methods and several baseline
methods in two distinct scenarios with unlabeled point sampling and a
fixed-size pool.
