Distributed Batch Gaussian Process Optimization

Erik A. Daxberger, Bryan Kian Hsiang Low
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:951-960, 2017.

Abstract

This paper presents a novel distributed batch Gaussian process upper confidence bound (DB-GP-UCB) algorithm for performing batch Bayesian optimization (BO) of highly complex, costly-to-evaluate black-box objective functions. In contrast to existing batch BO algorithms, DB-GP-UCB can jointly optimize a batch of inputs (as opposed to selecting the inputs of a batch one at a time) while still preserving scalability in the batch size. To realize this, we generalize GP-UCB to a new batch variant amenable to a Markov approximation, which can then be naturally formulated as a multi-agent distributed constraint optimization problem in order to fully exploit the efficiency of its state-of-the-art solvers for achieving linear time in the batch size. Our DB-GP-UCB algorithm offers practitioners the flexibility to trade off between the approximation quality and time efficiency by varying the Markov order. We provide a theoretical guarantee for the convergence rate of DB-GP-UCB via bounds on its cumulative regret. Empirical evaluation on synthetic benchmark objective functions and a real-world optimization problem shows that DB-GP-UCB outperforms the state-of-the-art batch BO algorithms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-daxberger17a, title = {Distributed Batch {G}aussian Process Optimization}, author = {Erik A. Daxberger and Bryan Kian Hsiang Low}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {951--960}, 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/daxberger17a/daxberger17a.pdf}, url = {https://proceedings.mlr.press/v70/daxberger17a.html}, abstract = {This paper presents a novel distributed batch Gaussian process upper confidence bound (DB-GP-UCB) algorithm for performing batch Bayesian optimization (BO) of highly complex, costly-to-evaluate black-box objective functions. In contrast to existing batch BO algorithms, DB-GP-UCB can jointly optimize a batch of inputs (as opposed to selecting the inputs of a batch one at a time) while still preserving scalability in the batch size. To realize this, we generalize GP-UCB to a new batch variant amenable to a Markov approximation, which can then be naturally formulated as a multi-agent distributed constraint optimization problem in order to fully exploit the efficiency of its state-of-the-art solvers for achieving linear time in the batch size. Our DB-GP-UCB algorithm offers practitioners the flexibility to trade off between the approximation quality and time efficiency by varying the Markov order. We provide a theoretical guarantee for the convergence rate of DB-GP-UCB via bounds on its cumulative regret. Empirical evaluation on synthetic benchmark objective functions and a real-world optimization problem shows that DB-GP-UCB outperforms the state-of-the-art batch BO algorithms.} }
Endnote
%0 Conference Paper %T Distributed Batch Gaussian Process Optimization %A Erik A. Daxberger %A Bryan Kian Hsiang Low %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-daxberger17a %I PMLR %P 951--960 %U https://proceedings.mlr.press/v70/daxberger17a.html %V 70 %X This paper presents a novel distributed batch Gaussian process upper confidence bound (DB-GP-UCB) algorithm for performing batch Bayesian optimization (BO) of highly complex, costly-to-evaluate black-box objective functions. In contrast to existing batch BO algorithms, DB-GP-UCB can jointly optimize a batch of inputs (as opposed to selecting the inputs of a batch one at a time) while still preserving scalability in the batch size. To realize this, we generalize GP-UCB to a new batch variant amenable to a Markov approximation, which can then be naturally formulated as a multi-agent distributed constraint optimization problem in order to fully exploit the efficiency of its state-of-the-art solvers for achieving linear time in the batch size. Our DB-GP-UCB algorithm offers practitioners the flexibility to trade off between the approximation quality and time efficiency by varying the Markov order. We provide a theoretical guarantee for the convergence rate of DB-GP-UCB via bounds on its cumulative regret. Empirical evaluation on synthetic benchmark objective functions and a real-world optimization problem shows that DB-GP-UCB outperforms the state-of-the-art batch BO algorithms.
APA
Daxberger, E.A. & Low, B.K.H.. (2017). Distributed Batch Gaussian Process Optimization. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:951-960 Available from https://proceedings.mlr.press/v70/daxberger17a.html.

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