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 proposed methods in diverse experiments.

翻译：贝叶斯优化因其能够高效寻找评估代价高昂的黑箱函数的全局最优解，已受到科学与工程领域众多研究方向的广泛关注。通常，概率回归模型被广泛用作代理函数，在给定输入和训练数据集的情况下，对函数评估的显式分布进行建模。除了基于概率回归的方法外，基于密度比估计的贝叶斯优化方法被提出，用于估计相对接近全局最优解与相对远离全局最优解的两组数据之间的密度比。沿着这一研究方向进一步拓展，有研究采用监督分类器来估计这两组数据的类别概率而非密度比。然而，该策略中使用的监督分类器容易对已知的全局解候选知识产生过度自信。假设我们能够获取未标记数据点（例如预定义的固定大小池），本文提出基于密度比估计的半监督学习贝叶斯优化方法以解决这一挑战。最后，我们在未标记点采样和固定大小池两种不同场景下展示了所提方法与若干基线方法的实证结果，并通过多样化的实验分析了所提方法的有效性。