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 $\nu$ 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 $d\ge 1$. Empirical validation suggests better performance and drastically improved computational scalablity compared with its predecessor, Improved GP-UCB.

Included an errata highlighting an omission in the proof of lemma 1 and pointing to a fix in the author's thesis; the omission does not affect the main result