Publications

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

José Miguel Hernández-Lobato, Matthew W. Hoffman, Zoubin Ghahramani, December 2014. (In Advances in Neural Information Processing Systems 28). Montreal, Canada.

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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 realworld 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.

Predictive Entropy Search for Bayesian Optimization with Unknown Constraints

José Miguel Hernández-Lobato, Michael A. Gelbart, Matthew W. Hoffman, Ryan P. Adams, Zoubin Ghahramani, 2015. (In 32nd International Conference on Machine Learning).

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Unknown constraints arise in many types of expensive black-box optimization problems. Several methods have been proposed recently for performing Bayesian optimization with constraints, based on the expected improvement (EI) heuristic. However, EI can lead to pathologies when used with constraints. For example, in the case of decoupled constraints—i.e., when one can independently evaluate the objective or the constraints—EI can encounter a pathology that prevents exploration. Additionally, computing EI requires a current best solution, which may not exist if none of the data collected so far satisfy the constraints. By contrast, information-based approaches do not suffer from these failure modes. In this paper, we present a new information-based method called Predictive Entropy Search with Constraints (PESC). We analyze the performance of PESC and show that it compares favorably to EI-based approaches on synthetic and benchmark problems, as well as several real-world examples. We demonstrate that PESC is an effective algorithm that provides a promising direction towards a unified solution for constrained Bayesian optimization.

On correlation and budget constraints in model-based bandit optimization with application to automatic machine learning

Matthew W Hoffman, Bobak Shahriari, Nando de Freitas, April 2014. (In 17th International Conference on Artificial Intelligence and Statistics). Reykjavik, Iceland.

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We address the problem of finding the maximizer of a nonlinear function that can only be evaluated, subject to noise, at a finite number of query locations. Further, we will assume that there is a constraint on the total number of permitted function evaluations. We introduce a Bayesian approach for this problem and show that it empirically outperforms both the existing frequentist counterpart and other Bayesian optimization methods. The Bayesian approach places emphasis on detailed modelling, including the modelling of correlations among the arms. As a result, it can perform well in situations where the number of arms is much larger than the number of allowed function evaluation, whereas the frequentist counterpart is inapplicable. This feature enables us to develop and deploy practical applications, such as automatic machine learning toolboxes. The paper presents comprehensive comparisons of the proposed approach with many Bayesian and bandit optimization techniques, the first comparison of many of these methods in the literature.

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