Bayesian optimization has demonstrated impressive success in finding the optimum location $x^{*}$ and value $f^{*}=f(x^{*})=\max_{x\in\mathcal{X}}f(x)$ of the black-box function $f$. In some applications, however, the optimum value is known in advance and the goal is to find the corresponding optimum location. Existing work in Bayesian optimization (BO) has not effectively exploited the knowledge of $f^{*}$ for optimization. In this paper, we consider a new setting in BO in which the knowledge of the optimum value is available. Our goal is to exploit the knowledge about $f^{*}$ to search for the location $x^{*}$ efficiently. To achieve this goal, we first transform the Gaussian process surrogate using the information about the optimum value. Then, we propose two acquisition functions, called confidence bound minimization and expected regret minimization, which exploit the knowledge about the optimum value to identify the optimum location efficiently. We show that our approaches work both intuitively and quantitatively achieve better performance against standard BO methods. We demonstrate real applications in tuning a deep reinforcement learning algorithm on the CartPole problem and XGBoost on Skin Segmentation dataset in which the optimum values are publicly available.

利用高斯过程代理转换和两种收集函数来有效地搜索输入量x*的新颖贝叶斯优化方法对调优深度强化学习算法和肤色分割数据集中的XGBoost模型进行了实验证明其相对于标准BO方法具有直观和数量上更好的性能。

贝叶斯优化中找到问题的解，但不确定其位置