Bandit optimisation of functions in the Matérn kernel RKHS

We consider the problem of optimising functions in the reproducing kernel Hilbert space (RKHS) of a Mat\érn kernel with smoothness parameter $\nu$ 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 $\nu>1$ and $d \geq 1$. Empirical validation suggests better performance and drastically improved computational scalablity compared with its predecessor, Improved GP-UCB.