Bandit Optimisation of Functions in the Matérn Kernel RKHS
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
Text
Janz et al. "Bandit Optimisation of Functions in the Matérn Kernel RKHS." Artificial Intelligence and Statistics, 2020.Markdown
[Janz et al. "Bandit Optimisation of Functions in the Matérn Kernel RKHS." Artificial Intelligence and Statistics, 2020.](https://mlanthology.org/aistats/2020/janz2020aistats-bandit/)BibTeX
@inproceedings{janz2020aistats-bandit,
title = {{Bandit Optimisation of Functions in the Matérn Kernel RKHS}},
author = {Janz, David and Burt, David and Gonzalez, Javier},
booktitle = {Artificial Intelligence and Statistics},
year = {2020},
pages = {2486-2495},
volume = {108},
url = {https://mlanthology.org/aistats/2020/janz2020aistats-bandit/}
}