On Convergence of Average-Reward Q-Learning in Weakly Communicating Markov Decision Processes
<|reference_start|>On Convergence of Average-Reward Q-Learning in Weakly Communicating Markov Decision Processes: This paper analyzes reinforcement learning (RL) algorithms for Markov decision processes (MDPs) under the average-reward criterion. We focus on Q-learning algorithms based on relative value iteration (RVI), which are model-free stochastic analogues of the classical RVI method for average-reward MDPs. These algorithms have low per-iteration complexity, making them well-suited for large state space problems. We extend the almost-sure convergence analysis of RVI Q-learning algorithms developed by Abounadi, Bertsekas, and Borkar (2001) from unichain to weakly communicating MDPs. This extension is important both practically and theoretically: weakly communicating MDPs cover a much broader range of applications compared to unichain MDPs, and their optimality equations have a richer solution structure (with multiple degrees of freedom), introducing additional complexity in proving algorithmic convergence. We also characterize the sets to which RVI Q-learning algorithms converge, showing that they are compact, connected, potentially nonconvex, and comprised of solutions to the average-reward optimality equation, with exactly one less degree of freedom than the general solution set of this equation. Furthermore, we extend our analysis to two RVI-based hierarchical average-reward RL algorithms using the options framework, proving their almost-sure convergence and characterizing their sets of convergence under the assumption that the underlying semi-Markov decision process is weakly communicating.<|reference_end|>
@article{wan2024on,
    title={On Convergence of Average-Reward Q-Learning in Weakly Communicating
  Markov Decision Processes},
    author={Yi Wan, Huizhen Yu, Richard S. Sutton},
    journal={arXiv preprint arXiv:2408.16262},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.16262},
    primaryClass={cs.LG math.OC}
}