# Momentum Q-learning with Finite-Sample Convergence Guarantee

Existing studies indicate that momentum ideas in conventional optimization can be used to improve the performance of Q-learning algorithms. However, the finite-sample analysis for momentum-based Q-learning algorithms is only available for the tabular case without function approximations. This paper analyzes a class of momentum-based Q-learning algorithms with finite-sample guarantee. Specifically, we propose the MomentumQ algorithm, which integrates the Nesterov's and Polyak's momentum schemes, and generalizes the existing momentum-based Q-learning algorithms. For the infinite state-action space case, we establish the convergence guarantee for MomentumQ with linear function approximations and Markovian sampling. In particular, we characterize the finite-sample convergence rate which is provably faster than the vanilla Q-learning. This is the first finite-sample analysis for momentum-based Q-learning algorithms with function approximations. For the tabular case under synchronous sampling, we also obtain a finite-sample convergence rate that is slightly better than the SpeedyQ <cit.> when choosing a special family of step sizes. Finally, we demonstrate through various experiments that the proposed MomentumQ outperforms other momentum-based Q-learning algorithms.

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