Bandit optimisation of functions in the Matérn kernel RKHS
This addresses the challenge of efficient optimization in high-dimensional spaces with noisy feedback, offering a practical solution with theoretical guarantees, though it appears incremental as an improvement over an existing method.
The paper tackled the problem of optimizing functions in the Matérn kernel RKHS under noisy bandit feedback, introducing the π-GP-UCB algorithm which achieves guaranteed sublinear regret for all ν>1 and d≥1, with empirical results showing better performance and drastically improved computational scalability compared to its predecessor.
We consider the problem of optimising functions in the reproducing kernel Hilbert space (RKHS) of a Matérn kernel with smoothness 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 $d \geq 1$. Empirical validation suggests better performance and drastically improved computational scalablity compared with its predecessor, Improved GP-UCB.