Efficient Kernel UCB for Contextual Bandits - Archive ouverte HAL Access content directly
Conference Papers Year : 2022

Efficient Kernel UCB for Contextual Bandits

Abstract

In this paper, we tackle the computational efficiency of kernelized UCB algorithms in contextual bandits. While standard methods require a $O(CT^3)$ complexity where $T$ is the horizon and the constant $C$ is related to optimizing the UCB rule, we propose an efficient contextual algorithm for large-scale problems. Specifically, our method relies on incremental Nyström approximations of the joint kernel embedding of contexts and actions. This allows us to achieve a complexity of $O(CT m^2)$ where $m$ is the number of Nyström points. To recover the same regret as the standard kernelized UCB algorithm, m needs to be of order of the effective dimension of the problem, which is at most $O(\sqrt{T})$ and nearly constant in some cases.
Fichier principal
Vignette du fichier
999.pdf (1.32 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03575953 , version 1 (15-02-2022)

Identifiers

  • HAL Id : hal-03575953 , version 1

Cite

Houssam Zenati, Alberto Bietti, Eustache Diemert, Julien Mairal, Matthieu Martin, et al.. Efficient Kernel UCB for Contextual Bandits. International Conference on Artificial Intelligence and Statistics, Mar 2022, Valencia, Spain. pp.5689-5720. ⟨hal-03575953⟩
109 View
109 Download

Share

Gmail Facebook X LinkedIn More