On Optimality of Myopic Policy for Restless Multi-armed Bandit Problem with Non i.i.d. Arms and Imperfect Detection

We consider the channel access problem in a multi-channel opportunistic communication system with imperfect channel sensing, where the state of each channel evolves as a non independent and identically distributed Markov process. This problem can be cast into a restless multi-armed bandit (RMAB) problem that is intractable for its exponential computation complexity. A natural alternative is to consider the easily implementable myopic policy that maximizes the immediate reward but ignores the impact of the current strategy on the future reward. In particular, we analyze a family of generic and practically important functions, termed as g-regular functions characterized by three axioms, and establish a set of closed-form structural conditions for the optimality of myopic policy. Index Terms Restless multi-armed bandit (RMAB), myopic policy, opportunistic spectrum access (OSA), Imperfect Detection