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We consider the problem of content caching at the wireless edge to serve aset of end users via unreliable wireless channels so as to minimize the averagelatency experienced by end users due to the constrained wireless edge cachecapacity. We formulate this problem as a Markov decision process, or morespecifically a restless multi-armed bandit problem, which is provably hard tosolve. We begin by investigating a discounted counterpart, and prove that itadmits an optimal policy of the threshold-type. We then show that this resultalso holds for average latency problem. Using this structural result, weestablish the indexability of our problem, and employ the Whittle index policyto minimize average latency. Since system parameters such as content requestrates and wireless channel conditions are often unknown and time-varying, wefurther develop a model-free reinforcement learning algorithm dubbed asQ^{+}-Whittle that relies on Whittle index policy. However, Q^{+}-Whittlerequires to store the Q-function values for all state-action pairs, the numberof which can be extremely large for wireless edge caching. To this end, weapproximate the Q-function by a parameterized function class with a muchsmaller dimension, and further design a Q^{+}-Whittle algorithm with linearfunction approximation, which is called Q^{+}-Whittle-LFA. We provide afinite-time bound on the mean-square error of Q^{+}-Whittle-LFA. Simulationresults using real traces demonstrate that Q^{+}-Whittle-LFA yields excellentempirical performance.

Whittle Index based Q-Learning for Wireless Edge Caching with Linear Function Approximation