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.


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.

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