Predictive Entropy Search for Bayesian Optimization with Unknown Constraints
Hernández-Lobato, José Miguel
Gelbart, Michael A
Hoffman, Matthew W
Adams, Ryan P
Proceedings of The 32nd International Conference on Machine Learning
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Hernández-Lobato, J. M., Gelbart, M. A., Hoffman, M. W., Adams, R. P., & Ghahramani, Z. (2015). Predictive Entropy Search for Bayesian Optimization with Unknown Constraints. Proceedings of The 32nd International Conference on Machine Learning, 1699-1707. http://jmlr.org/proceedings/papers/v37/hernandez-lobatob15.html
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, informationbased 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.
José Miguel Hernández-Lobato acknowledges support from the Rafael del Pino Foundation. Zoubin Ghahramani acknowledges support from Google Focused Research Award and EPSRC grant EP/I036575/1. Matthew W. Hoffman acknowledges support from EPSRC grant EP/J012300/1.
This record's URL: https://www.repository.cam.ac.uk/handle/1810/248993
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Licence URL: http://creativecommons.org/licenses/by-nc/2.0/uk/
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