Predictive Entropy Search for Bayesian Optimization with Unknown Constraints

Jose Miguel Hernandez-Lobato, Michael Gelbart, Matthew Hoffman, Ryan Adams, Zoubin Ghahramani
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:1699-1707, 2015.

Abstract

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.

Cite this Paper


BibTeX
@InProceedings{pmlr-v37-hernandez-lobatob15, title = {Predictive Entropy Search for Bayesian Optimization with Unknown Constraints}, author = {Hernandez-Lobato, Jose Miguel and Gelbart, Michael and Hoffman, Matthew and Adams, Ryan and Ghahramani, Zoubin}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {1699--1707}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/hernandez-lobatob15.pdf}, url = { http://proceedings.mlr.press/v37/hernandez-lobatob15.html }, abstract = {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.} }
Endnote
%0 Conference Paper %T Predictive Entropy Search for Bayesian Optimization with Unknown Constraints %A Jose Miguel Hernandez-Lobato %A Michael Gelbart %A Matthew Hoffman %A Ryan Adams %A Zoubin Ghahramani %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-hernandez-lobatob15 %I PMLR %P 1699--1707 %U http://proceedings.mlr.press/v37/hernandez-lobatob15.html %V 37 %X 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.
RIS
TY - CPAPER TI - Predictive Entropy Search for Bayesian Optimization with Unknown Constraints AU - Jose Miguel Hernandez-Lobato AU - Michael Gelbart AU - Matthew Hoffman AU - Ryan Adams AU - Zoubin Ghahramani BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-hernandez-lobatob15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 1699 EP - 1707 L1 - http://proceedings.mlr.press/v37/hernandez-lobatob15.pdf UR - http://proceedings.mlr.press/v37/hernandez-lobatob15.html AB - 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. ER -
APA
Hernandez-Lobato, J.M., Gelbart, M., Hoffman, M., Adams, R. & Ghahramani, Z.. (2015). Predictive Entropy Search for Bayesian Optimization with Unknown Constraints. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:1699-1707 Available from http://proceedings.mlr.press/v37/hernandez-lobatob15.html .

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