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

TL;DR

Predictive Entropy Search (PES) is a new Bayesian optimization method that efficiently selects evaluation points by maximizing expected information gain, improving accuracy over previous methods like Entropy Search.

Contribution

PES introduces a more accurate and efficient information-theoretic acquisition function for Bayesian optimization, with the ability to fully Bayesian treat hyperparameters.

Findings

PES outperforms Entropy Search in synthetic and real-world tasks.

PES achieves faster convergence and better optimization results.

PES is applicable across diverse fields like machine learning, finance, and robotics.

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.