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Restless bandit problems are instances of non-stationary multi-armed bandits.These problems have been studied well from the optimization perspective, wherethe goal is to efficiently find a near-optimal policy when system parametersare known. However, very few papers adopt a learning perspective, where theparameters are unknown. In this paper, we analyze the performance of Thompsonsampling in episodic restless bandits with unknown parameters. We consider ageneral policy map to define our competitor and prove an$\tilde{\mathcal{O}}(\sqrt{T})$ Bayesian regret bound. Our competitor isflexible enough to represent various benchmarks including the best fixed actionpolicy, the optimal policy, the Whittle index policy, or the myopic policy. Wealso present empirical results that support our theoretical findings.

Regret Bounds for Thompson Sampling in Episodic Restless Bandit Problems