Gaussian Process based Bayesian Optimization is a well-known sample efficient sequential strategy for globally optimizing black-box, expensive, and multi-extremal functions. The role of the Gaussian Process is to provide a probabilistic approximation of the unknown function, depending on the sequentially collected observations, while an acquisition function drives the choice of the next solution to evaluate, balancing between exploration and exploitation, depending on the current Gaussian Process model. Despite the huge effort of the scientific community in defining effective exploration-exploitation mechanisms, we are still far away from the master acquisition function. This paper merges the most relevant results and insights from both algorithmic and human search strategies to propose a novel acquisition function, mastering the trade-off between explorative and exploitative choices, adaptively. We compare the proposed acquisition function on a number of test functions and against different state-of-the-art ones, which are instead based on prefixed or random scheduling between exploration and exploitation. A Pareto analysis is performed with respect to two (antagonistic) goals: convergence to the optimum and exploration capability. Results empirically prove that the proposed acquisition function is almost always Pareto optimal and also the most balanced trade-off between the two goals.

翻译：基于高斯过程的贝叶斯优化是一种著名的样本高效序贯策略，用于全局优化黑箱、昂贵且多极值的函数。高斯过程的作用是根据序贯收集的观测值提供未知函数的概率近似，而采集函数则基于当前高斯过程模型，在探索与利用之间取得平衡，驱动下一解的评价选择。尽管学术界在定义有效的探索-利用机制上付出了巨大努力，我们距离"最优采集函数"仍有差距。本文融合了算法搜索策略与人类搜索策略中最相关的研究成果与洞见，提出了一种新型采集函数，能够自适应地掌握探索性与利用性选择之间的权衡。我们在多个测试函数上将该采集函数与多种基于固定或随机调度探索-利用的现有最优方法进行了比较。针对两个（互斥的）目标——收敛至最优解与探索能力——进行了帕累托分析。实验结果证明，所提采集函数几乎始终是帕累托最优的，并且也是两个目标之间最平衡的权衡方案。