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.

翻译：贝叶斯优化因其能够高效找到昂贵黑箱函数的全局最优解，已引起科学和工程领域众多研究者的广泛关注。通常，概率回归模型（如高斯过程和贝叶斯神经网络）被广泛用作替代函数，以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。除基于概率回归的贝叶斯优化外，还提出了基于密度比估计的贝叶斯优化方法，用于估计相对接近与相对远离全局最优解的两类数据点的密度比。为了进一步拓展该研究方向，可以采用监督分类器来估计这两类数据点的类别概率，而非直接估计密度比。然而，该策略中使用的监督分类器容易对全局解候选者产生过度自信。针对这一问题，我们提出了一种基于密度比估计的半监督学习贝叶斯优化方法。最后，我们在具有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验结果。