Predictive Entropy Search for Efficient Global Optimization of Black-box Functions

TLDR

The authors introduce Predictive Entropy Search (PES), an information‑theoretic Bayesian optimization method. PES iteratively selects evaluation points by maximizing expected information gain about the global maximum, expressed as the expected reduction in predictive differential entropy, and is tested on synthetic and real‑world problems across machine learning, finance, biotechnology, and robotics. PES achieves higher accuracy and efficiency than Entropy Search, supports full Bayesian hyperparameter treatment, and yields significant performance improvements in optimization tasks.

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.