Max-value Entropy Search for Efficient Bayesian Optimization

Zi Wang, Stefanie Jegelka
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:3627-3635, 2017.

Abstract

Entropy Search (ES) and Predictive Entropy Search (PES) are popular and empirically successful Bayesian Optimization techniques. Both rely on a compelling information-theoretic motivation, and maximize the information gained about the $\arg\max$ of the unknown function; yet, both are plagued by the expensive computation for estimating entropies. We propose a new criterion, Max-value Entropy Search (MES), that instead uses the information about the maximum function value. We show relations of MES to other Bayesian optimization methods, and establish a regret bound. We observe that MES maintains or improves the good empirical performance of ES/PES, while tremendously lightening the computational burden. In particular, MES is much more robust to the number of samples used for computing the entropy, and hence more efficient for higher dimensional problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-wang17e, title = {Max-value Entropy Search for Efficient {B}ayesian Optimization}, author = {Zi Wang and Stefanie Jegelka}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {3627--3635}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/wang17e/wang17e.pdf}, url = {https://proceedings.mlr.press/v70/wang17e.html}, abstract = {Entropy Search (ES) and Predictive Entropy Search (PES) are popular and empirically successful Bayesian Optimization techniques. Both rely on a compelling information-theoretic motivation, and maximize the information gained about the $\arg\max$ of the unknown function; yet, both are plagued by the expensive computation for estimating entropies. We propose a new criterion, Max-value Entropy Search (MES), that instead uses the information about the maximum function value. We show relations of MES to other Bayesian optimization methods, and establish a regret bound. We observe that MES maintains or improves the good empirical performance of ES/PES, while tremendously lightening the computational burden. In particular, MES is much more robust to the number of samples used for computing the entropy, and hence more efficient for higher dimensional problems.} }
Endnote
%0 Conference Paper %T Max-value Entropy Search for Efficient Bayesian Optimization %A Zi Wang %A Stefanie Jegelka %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-wang17e %I PMLR %P 3627--3635 %U https://proceedings.mlr.press/v70/wang17e.html %V 70 %X Entropy Search (ES) and Predictive Entropy Search (PES) are popular and empirically successful Bayesian Optimization techniques. Both rely on a compelling information-theoretic motivation, and maximize the information gained about the $\arg\max$ of the unknown function; yet, both are plagued by the expensive computation for estimating entropies. We propose a new criterion, Max-value Entropy Search (MES), that instead uses the information about the maximum function value. We show relations of MES to other Bayesian optimization methods, and establish a regret bound. We observe that MES maintains or improves the good empirical performance of ES/PES, while tremendously lightening the computational burden. In particular, MES is much more robust to the number of samples used for computing the entropy, and hence more efficient for higher dimensional problems.
APA
Wang, Z. & Jegelka, S.. (2017). Max-value Entropy Search for Efficient Bayesian Optimization. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:3627-3635 Available from https://proceedings.mlr.press/v70/wang17e.html.

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