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In this paper we present a model for the hidden Markovian bandit problem withlinear rewards. As opposed to current work on Markovian bandits, we do notassume that the state is known to the decision maker before making thedecision. Furthermore, we assume structural side information where the decisionmaker knows in advance that there are two types of hidden states; one is commonto all arms and evolves according to a Markovian distribution, and the other isunique to each arm and is distributed according to an i.i.d. process that isunique to each arm. We present an algorithm and regret analysis to thisproblem. Surprisingly, we can recover the hidden states and maintainlogarithmic regret in the case of a convex polytope action set. Furthermore, weshow that the structural side information leads to expected regret that doesnot depend on the number of extreme points in the action space. Therefore, weobtain practical solutions even in high dimensional problems.

The Restless Hidden Markov Bandit with Linear Rewards and Side Information