Density Ratio Estimation-based Bayesian Optimization with Semi-Supervised Learning

Bayesian optimization has attracted huge attention from diverse research areas in science and engineering, since it is capable of efficiently finding a global optimum of an expensive-to-evaluate black-box function. In general, a probabilistic regression model 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 methods, 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, supervised classifiers are 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 known knowledge on global solution candidates. Supposing that we have access to unlabeled points, e.g., predefined fixed-size pools, we propose density ratio estimation-based Bayesian optimization with semi-supervised learning to solve this challenge. Finally, we show the empirical results of our methods and several baseline methods in two distinct scenarios with unlabeled point sampling and a fixed-size pool, and analyze the validity of our methods in diverse experiments.

Finding global solutions to problems involving expensive-to-evaluate black-box functions is a key research topic in science and engineering. Bayesian optimization is an effective method for addressing such problems, typically using a probabilistic regression model as a surrogate model. More recently, density ratio estimation-based Bayesian optimization has enabled the use of supervised classifiers. However, these classifiers tend to be overconfident for known knowledge on global solution candidates. To tackle this issue, we propose a density ratio estimation-based Bayesian optimization method with semi-supervised learning, making use of unlabeled data obtained from predefined fixed-size pools or unlabeled point sampling.