Learning the Model While Learning Q: Finite-Time Sample Complexity of Online SyncMBQ

Reinforcement learning has witnessed significant advancements, particularly with the emergence of model-based approaches. Among these, $Q$-learning has proven to be a powerful algorithm in model-free settings. However, the extension of $Q$-learning to a model-based framework remains relatively unexplored. In this paper, we investigate the sample complexity of $Q$-learning when integrated with a model-based approach. The proposed algorihtms learns both the model and Q-value in an online manner. We demonstrate a near-optimal sample complexity result within a broad range of step sizes.