A Restless Bandit Formulation of Opportunistic Access: Indexablity and Index Policy

We focus on an opportunistic communication system consisting of multiple independent channels with time-varying states. With limited sensing, a user can only sense and access a subset of channels and accrue rewards determined by the state of the sensed channels. We formulate the problem of optimal sequential channel probing as a restless multi-armed bandit process, for which a powerful index policy-Whittle's index policy-can be implemented based on the indexability of the system. Exploiting the underlying structure of the multi-channel opportunistic access problem, we establish the indexability and obtain the Whittle's index in closed-form, which leads to a direct implementation of Whittle's index policy with little complexity. Furthermore, we show that Whittle's index policy is equivalent to the myopic policy when channels are statistically identical.