Non-asymptotic Convergence of Average-reward Q-learning with Options

Abstract:We study the finite-sample convergence of Q-learning algorithms for the average-reward formulation of Reinforcement Learning (RL) with options. While options allow temporarily extended and hierarchical actions, the average-reward formulation incorporates continual tasks beyond discounted and episodic RL. We establish the first $\tilde{O}(1/\text{iterations})$ convergence guarantees, in the mean-square sense, for average-reward option Q-learning algorithms in both the inter- and intra-option settings. First, we prove that both inter- and intra-option Bellman operators satisfy multi-step span contractions under unichain assumptions. Then, we propose synchronous estimators of these multi-step option Bellman operators leading to two variants of option Q-learning. Finally, we extend the stochastic approximation framework to prove convergence rates of these two algorithms under the minimal assumptions used in the literature.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2610.20347 [cs.LG]

(or arXiv:2610.20347v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.20347 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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