Under the Markov-Averaged Indexability condition, synchronous Q-learning with Whittle indices converges almost surely to the optimal Q-function and indices in restless bandits whose arms are driven by an unobserved latent Markov environment.
Stochastic multi-armed- bandit problem with non-stationary rewards,
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MARBLE: Multi-Armed Restless Bandits in Latent Markovian Environment
Under the Markov-Averaged Indexability condition, synchronous Q-learning with Whittle indices converges almost surely to the optimal Q-function and indices in restless bandits whose arms are driven by an unobserved latent Markov environment.