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This paper addresses an important class of restless multi-armed bandit (RMAB)problems that finds a broad application area in operations research, stochasticoptimization, and reinforcement learning. There are $N$ independent Markovprocesses that may be operated, observed and offer rewards. Due to the resourceconstraint, we can only choose a subset of $M~(M<N)$ processes to operate andaccrue reward determined by the states of selected processes. We formulate theproblem as a partially observable RMAB with an infinite state space and designan algorithm that achieves a near-optimal performance with low complexity. Ouralgorithm is based on a generalization of Whittle's original idea ofindexability. Referred to as the relaxed indexability, the extended definitionleads to the efficient online verifications and computations of the approximateWhittle index under the proposed algorithmic framework.

Relaxed Indexability and Index Policy for Partially Observable Restless Bandits