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, random forests, 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 tend to be overconfident for a global solution candidate. To solve this overconfidence 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地找到昂贵黑箱函数的全局最优解，而吸引了科学和工程领域众多研究者的关注。通常，概率回归模型（如高斯过程、随机森林和贝叶斯神经网络）被广泛用作代理函数，用于在给定输入估计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，研究者还提出了基于密度比估计的贝叶斯优化，用于估计相对接近和相对远离全局最优解的两组数据之间的密度比。在这一研究方向的基础上，可采用监督分类器估计这两组数据的类别概率，替代密度比估计。然而，该策略中使用的监督分类器往往对全局解候选过度自信。为解决这一过度自信问题，我们提出了结合半监督学习的基于密度比估计的贝叶斯优化方法。最后，我们在两种不同场景（包含无标签点采样和固定规模池化）中，展示了所提出方法与若干基线方法的实验结果。