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We consider a linear stochastic bandit problem where the dimension $K$ of theunknown parameter $\theta$ is larger than the sampling budget $n$. In suchcases, it is in general impossible to derive sub-linear regret bounds sinceusual linear bandit algorithms have a regret in $O(K\sqrt{n})$. In this paperwe assume that $\theta$ is $S-$sparse, i.e. has at most $S-$non-zerocomponents, and that the space of arms is the unit ball for the $||.||_2$ norm.We combine ideas from Compressed Sensing and Bandit Theory and derivealgorithms with regret bounds in $O(S\sqrt{n})$.

Bandit Theory meets Compressed Sensing for high dimensional Stochastic Linear Bandit