This paper addresses an important class of restless multi-armed bandit (RMAB) problems that finds a broad application area in operations research, stochastic optimization, and reinforcement learning. There are $N$ independent Markov processes that may be operated, observed and offer rewards. Due to the resource constraint, we can only choose a subset of $M~(M<N)$ processes to operate and accrue reward determined by the states of selected processes. We formulate the problem as an RMAB with an infinite state space and design an algorithm that achieves a near-optimal performance with low complexity. Our algorithm is based on Whittles original idea of index policy but can be implemented under more general scenarios, including continuous state space, relaxed indexability, online computations, etc.
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