Portfolio Allocation for Bayesian Optimization

Eric Brochu, Matthew W. Hoffman, Nando de Freitas
Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, PMLR R9:365-384, 2011.

Abstract

Bayesian optimization with Gaussian processes has become an increasingly popular tool in the machine learning community. It is efficient and can be used when very little is known about the objective function, making it popular in expensive black-box optimization scenarios. It uses Bayesian methods to sample the objective efficiently using an acquisition function which incorporates the model’s estimate of the objective and the uncertainty at any given point. However, there are several different parameterized acquisition functions in the literature, and it is often unclear which one to use. Instead of using a single acquisition function, we adopt a portfolio of acquisition functions governed by an online multi-armed bandit strategy. We propose several portfolio strategies, the best of which we call GP-Hedge, and show that this method outperforms the best individual acquisition function. We also provide a theoretical bound on the algorithm’s performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR9-brochu11a, title = {Portfolio Allocation for {B}ayesian Optimization}, author = {Brochu, Eric and Hoffman, Matthew W. and de Freitas, Nando}, booktitle = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence}, pages = {365--384}, year = {2011}, editor = {Cozman, Fabio and Pfeffer, Avi}, volume = {R9}, series = {Proceedings of Machine Learning Research}, month = {14--17 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r9/main/assets/brochu11a/brochu11a.pdf}, url = {https://proceedings.mlr.press/r9/brochu11a.html}, abstract = {Bayesian optimization with Gaussian processes has become an increasingly popular tool in the machine learning community. It is efficient and can be used when very little is known about the objective function, making it popular in expensive black-box optimization scenarios. It uses Bayesian methods to sample the objective efficiently using an acquisition function which incorporates the model’s estimate of the objective and the uncertainty at any given point. However, there are several different parameterized acquisition functions in the literature, and it is often unclear which one to use. Instead of using a single acquisition function, we adopt a portfolio of acquisition functions governed by an online multi-armed bandit strategy. We propose several portfolio strategies, the best of which we call GP-Hedge, and show that this method outperforms the best individual acquisition function. We also provide a theoretical bound on the algorithm’s performance.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Portfolio Allocation for Bayesian Optimization %A Eric Brochu %A Matthew W. Hoffman %A Nando de Freitas %B Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2011 %E Fabio Cozman %E Avi Pfeffer %F pmlr-vR9-brochu11a %I PMLR %P 365--384 %U https://proceedings.mlr.press/r9/brochu11a.html %V R9 %X Bayesian optimization with Gaussian processes has become an increasingly popular tool in the machine learning community. It is efficient and can be used when very little is known about the objective function, making it popular in expensive black-box optimization scenarios. It uses Bayesian methods to sample the objective efficiently using an acquisition function which incorporates the model’s estimate of the objective and the uncertainty at any given point. However, there are several different parameterized acquisition functions in the literature, and it is often unclear which one to use. Instead of using a single acquisition function, we adopt a portfolio of acquisition functions governed by an online multi-armed bandit strategy. We propose several portfolio strategies, the best of which we call GP-Hedge, and show that this method outperforms the best individual acquisition function. We also provide a theoretical bound on the algorithm’s performance. %Z Reissued by PMLR on 04 October 2026.
APA
Brochu, E., Hoffman, M.W. & de Freitas, N.. (2011). Portfolio Allocation for Bayesian Optimization. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R9:365-384 Available from https://proceedings.mlr.press/r9/brochu11a.html. Reissued by PMLR on 04 October 2026.

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