Nonmyopic Gaussian Process Optimization with Macro-Actions

Dmitrii Kharkovskii, Chun Kai Ling, Bryan Kian Hsiang Low
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:4593-4604, 2020.

Abstract

This paper presents a multi-staged approach to nonmyopic adaptive Gaussian process optimization (GPO) for Bayesian optimization (BO) of unknown, highly complex objective functions that, in contrast to existing nonmyopic adaptive BO algorithms, exploits the notion of macro-actions for scaling up to a further lookahead to match up to a larger available budget. To achieve this, we generalize GP upper confidence bound to a new acquisition function defined w.r.t. a nonmyopic adaptive macro-action policy, which is intractable to be optimized exactly due to an uncountable set of candidate outputs. The contribution of our work here is thus to derive a nonmyopic adaptive epsilon-Bayes-optimal macro-action GPO (epsilon-Macro-GPO) policy. To perform nonmyopic adaptive BO in real time, we then propose an asymptotically optimal anytime variant of our epsilon-Macro-GPO policy with a performance guarantee. We empirically evaluate the performance of our epsilon-Macro-GPO policy and its anytime variant in BO with synthetic and real-world datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-kharkovskii20a, title = {Nonmyopic Gaussian Process Optimization with Macro-Actions}, author = {Kharkovskii, Dmitrii and Ling, Chun Kai and Low, Bryan Kian Hsiang}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {4593--4604}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/kharkovskii20a/kharkovskii20a.pdf}, url = {https://proceedings.mlr.press/v108/kharkovskii20a.html}, abstract = {This paper presents a multi-staged approach to nonmyopic adaptive Gaussian process optimization (GPO) for Bayesian optimization (BO) of unknown, highly complex objective functions that, in contrast to existing nonmyopic adaptive BO algorithms, exploits the notion of macro-actions for scaling up to a further lookahead to match up to a larger available budget. To achieve this, we generalize GP upper confidence bound to a new acquisition function defined w.r.t. a nonmyopic adaptive macro-action policy, which is intractable to be optimized exactly due to an uncountable set of candidate outputs. The contribution of our work here is thus to derive a nonmyopic adaptive epsilon-Bayes-optimal macro-action GPO (epsilon-Macro-GPO) policy. To perform nonmyopic adaptive BO in real time, we then propose an asymptotically optimal anytime variant of our epsilon-Macro-GPO policy with a performance guarantee. We empirically evaluate the performance of our epsilon-Macro-GPO policy and its anytime variant in BO with synthetic and real-world datasets.} }
Endnote
%0 Conference Paper %T Nonmyopic Gaussian Process Optimization with Macro-Actions %A Dmitrii Kharkovskii %A Chun Kai Ling %A Bryan Kian Hsiang Low %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-kharkovskii20a %I PMLR %P 4593--4604 %U https://proceedings.mlr.press/v108/kharkovskii20a.html %V 108 %X This paper presents a multi-staged approach to nonmyopic adaptive Gaussian process optimization (GPO) for Bayesian optimization (BO) of unknown, highly complex objective functions that, in contrast to existing nonmyopic adaptive BO algorithms, exploits the notion of macro-actions for scaling up to a further lookahead to match up to a larger available budget. To achieve this, we generalize GP upper confidence bound to a new acquisition function defined w.r.t. a nonmyopic adaptive macro-action policy, which is intractable to be optimized exactly due to an uncountable set of candidate outputs. The contribution of our work here is thus to derive a nonmyopic adaptive epsilon-Bayes-optimal macro-action GPO (epsilon-Macro-GPO) policy. To perform nonmyopic adaptive BO in real time, we then propose an asymptotically optimal anytime variant of our epsilon-Macro-GPO policy with a performance guarantee. We empirically evaluate the performance of our epsilon-Macro-GPO policy and its anytime variant in BO with synthetic and real-world datasets.
APA
Kharkovskii, D., Ling, C.K. & Low, B.K.H.. (2020). Nonmyopic Gaussian Process Optimization with Macro-Actions. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:4593-4604 Available from https://proceedings.mlr.press/v108/kharkovskii20a.html.

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