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Reports (Technical Report) Year : 2012

## Bandit Theory meets Compressed Sensing for high dimensional Stochastic Linear Bandit

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Alexandra Carpentier
• Function : Author
• PersonId : 910455
Rémi Munos
• Function : Author
• PersonId : 836863

#### Abstract

We consider a linear stochastic bandit problem where the dimension $K$ of the unknown parameter $\theta$ 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 $\theta$ 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 $O(S\sqrt{n})$.

### Dates and versions

hal-00659731 , version 1 (13-01-2012)
hal-00659731 , version 2 (16-05-2012)

### Identifiers

• HAL Id : hal-00659731 , version 2
• ARXIV :

### Cite

Alexandra Carpentier, Rémi Munos. Bandit Theory meets Compressed Sensing for high dimensional Stochastic Linear Bandit. [Technical Report] 2012. ⟨hal-00659731v2⟩

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