Bandit optimisation of functions in the Matérn kernel RKHS
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.