Predictive Entropy Search for Efficient Global Optimization of Black-box Functions
José Miguel Hernández-Lobato University of Cambridge、Matthew W. Hoffman University of Cambridge、Zoubin Ghahramani University of Cambridge
Abstract
We propose a novel information-theoretic approach for Bayesian optimization called Predictive Entropy Search (PES). At each iteration, PES selects the next evaluation point that maximizes the expected information gained with respect to the global maximum. PES codifies this intractable acquisition function in terms of the expected reduction in the differential entropy of the predictive distribution. This reformulation allows PES to obtain approximations that are both more accurate and efficient than other alternatives such as Entropy Search (ES). Furthermore, PES can easily perform a fully Bayesian treatment of the model hyperparameters while ES cannot. We evaluate PES in both synthetic and real-world applications, including optimization problems in machine learning, finance, biotechnology, and robotics. We show that the increased accuracy of PES leads to significant gains in optimization performance.
中文速览
贝叶斯优化的核心难题在于：每次选下一个采样点时，怎样才能最快地找到黑箱函数的全局最优解？预测熵搜索（Predictive Entropy Search，PES）用信息论的角度来回答这个问题——每次选择那个能最大程度减少"全局最优点在哪里"这一不确定性的采样点。为了让这个原本难以计算的目标函数变得可处理，PES 把它改写成预测分布熵的对称形式，再借助随机特征近似（random feature approximation）从全局最优点的后验分布中采样，并用期望传播（Expectation Propagation，EP）来逼近条件熵，整个流程比此前的熵搜索（Entropy Search，ES）方法更准确也更高效，还能自然地对模型超参数做完全贝叶斯处理。在机器学习调参、金融、生物技术和机器人等多个合成与真实任务上的实验表明，PES 的近似精度提升直接转化为更好的优化性能，用更少的函数评估次数找到更好的解，这对那些每次评估代价极高的实际问题意义重大。
原文 arXiv:1406.2541;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1406.2541v1