Bandit optimisation of functions in the Matérn kernel RKHS

David Janz, David Burt, Javier Gonzalez
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:2486-2495, 2020.

Abstract

We consider the problem of optimising functions in the reproducing kernel Hilbert space (RKHS) of a Matérn kernel with smoothness parameter $u$ over the domain $[0,1]^d$ under noisy bandit feedback. Our contribution, the $\pi$-GP-UCB algorithm, is the first practical approach with guaranteed sublinear regret for all $u>1$ and $d \geq 1$. Empirical validation suggests better performance and drastically improved computational scalablity compared with its predecessor, Improved GP-UCB.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-janz20a, title = {Bandit optimisation of functions in the Matérn kernel RKHS}, author = {Janz, David and Burt, David and Gonzalez, Javier}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {2486--2495}, 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/janz20a/janz20a.pdf}, url = {https://proceedings.mlr.press/v108/janz20a.html}, abstract = {We consider the problem of optimising functions in the reproducing kernel Hilbert space (RKHS) of a Matérn kernel with smoothness parameter $u$ over the domain $[0,1]^d$ under noisy bandit feedback. Our contribution, the $\pi$-GP-UCB algorithm, is the first practical approach with guaranteed sublinear regret for all $u>1$ and $d \geq 1$. Empirical validation suggests better performance and drastically improved computational scalablity compared with its predecessor, Improved GP-UCB.} }
Endnote
%0 Conference Paper %T Bandit optimisation of functions in the Matérn kernel RKHS %A David Janz %A David Burt %A Javier Gonzalez %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-janz20a %I PMLR %P 2486--2495 %U https://proceedings.mlr.press/v108/janz20a.html %V 108 %X We consider the problem of optimising functions in the reproducing kernel Hilbert space (RKHS) of a Matérn kernel with smoothness parameter $u$ over the domain $[0,1]^d$ under noisy bandit feedback. Our contribution, the $\pi$-GP-UCB algorithm, is the first practical approach with guaranteed sublinear regret for all $u>1$ and $d \geq 1$. Empirical validation suggests better performance and drastically improved computational scalablity compared with its predecessor, Improved GP-UCB.
APA
Janz, D., Burt, D. & Gonzalez, J.. (2020). Bandit optimisation of functions in the Matérn kernel RKHS. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:2486-2495 Available from https://proceedings.mlr.press/v108/janz20a.html.

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