Preprintgreen2014

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

José Miguel Hernández-Lobato · Matthew W. Hoffman · Zoubin Ghahramani A

162 citations0/0 files storedarXiv (Cornell University)

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Advanced Bandit Algorithms Research Advanced Multi-Objective Optimization Algorithms Gaussian Processes and Bayesian Inference

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.

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References

2012Practical Bayesian Optimization of Machine Learning Algorithms 2012Information-Theoretic Regret Bounds for Gaussian Process Optimization in the Bandit Setting 2010A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning 2011An Empirical Evaluation of Thompson Sampling 2006The Copula-GARCH model of conditional dependencies: An international stock market application 2012Entropy search for information-efficient global optimization 2008Bayesian Inference and Optimal Design for the Sparse Linear Model 2008Practical Bayesian optimization

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