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The authors consider the Restless Multi-Armed Bandit (RMAB) problem with unknown dynamics in which a player chooses one out of N arms to play at each time. The reward state of each arm transits according to an unknown Markovian rule when it is played and evolves according to an arbitrary unknown random process when it is passive. The performance of an arm selection policy is measured by regret, defined as the reward loss with respect to the case where the player knows which arm is the most rewarding and always plays the best arm. They construct a policy with an interleaving exploration and exploitation epoch structure that achieves a regret with logarithmic order when arbitrary (but nontrivial) bounds on certain system parameters are known.
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