Year: 2012
Type: preprint
Abstract: We consider a linear stochastic bandit problem where the dimension $K$ of the unknown parameter $θ$ is larger than the sampling budget $n$. In such cases, it is in general impossible to derive sub-linear regret bounds since usual linear bandit algorithms have a regret in $O(K\sqrt{n})$. In this paper we assume that $θ$ is $S-$sparse, i.e. has at most $S-$non-zero components, and that the space of arms is the unit ball for the $||.||_2$ norm. We combine ideas from Compressed Sensing and Bandit Theory and derive algorithms with regret bounds in $O(S\sqrt{n})$.
Source: arXiv (Cornell University)
Authors: Carpentier, Alexandra, Munos, Rémi
Institution: Centre Inria de l'Université de Lille
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
Award: G1391404679
OpenAlex ID: W7097425697