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 Matérn family kernel with parameter ν over the domain [0,1]^d under noisy bandit feedback. Our contribution, the π-GP-UCB algorithm, is the first practical approach with guaranteed sublinear regret for all ν>1 and d ≥ 1. Empirical validation suggests better performance and drastically improved computational scalablity compared with its predecessor, Improved GP-UCB.
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