Bandit optimisation of functions in the Mat\'ern kernel RKHS

David Janz; David R. Burt; Javier González

Bandit optimisation of functions in the Mat\'ern kernel RKHS

Machine Learning 2023-02-28 v3 Machine Learning

Authors: David Janz , David R. Burt , Javier González

Abstract

We consider the problem of optimising functions in the reproducing kernel Hilbert space (RKHS) of a Mat\'ern 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.

Cite

@article{arxiv.2001.10396,
  title  = {Bandit optimisation of functions in the Mat\'ern kernel RKHS},
  author = {David Janz and David R. Burt and Javier González},
  journal= {arXiv preprint arXiv:2001.10396},
  year   = {2023}
}

Comments

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

Bandit optimisation of functions in the Mat\'ern kernel RKHS

Abstract

Cite

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