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$Q$-learning with function approximation is one of the most empiricallysuccessful while theoretically mysterious reinforcement learning (RL)algorithms, and was identified in Sutton (1999) as one of the most importanttheoretical open problems in the RL community. Even in the basic linearfunction approximation setting, there are well-known divergent examples. Inthis work, we show that \textit{target network} and \textit{truncation}together are enough to provably stabilize $Q$-learning with linear functionapproximation, and we establish the finite-sample guarantees. The resultimplies an $O(\epsilon^{-2})$ sample complexity up to a function approximationerror. Moreover, our results do not require strong assumptions or modifying theproblem parameters as in existing literature.

Target Network and Truncation Overcome The Deadly Triad in $Q$-Learning