One of the phenomena of interest is that Q-learning (Watkins, 1989) is known to suffer from overestimation issues, since it takes a maximum operator overaset ofestimated action-values.

This paper considers the problem of designing optimal algorithms for reinforcement learning in two-player zero-sum games. We focus on self-play algorithms which learn theoptimal policy by playing againstitself without any direct supervision.

Average-reward reinforcement learning offers a principled framework for long-term decision-making by maximizing the mean reward per time step. Although Q-learning is a widely used model-free algorithm with established sample complexity in discounted and finite-horizon Markov decision processes (MDPs), its theoretical guarantees for average-reward settings remain limited. This work studies a simple but effective Q-learning algorithm for average-reward MDPs with finite state and action spaces under the weakly communicating assumption, covering both single-agent and federated scenarios. For the single-agent case, we show that Q-learning with carefully chosen parameters achieves sample complexity $\widetilde{O}\left(\frac{|\mathcal{S}||\mathcal{A}|\|h^{\star}\|_{\mathsf{sp}}^3}{\varepsilon^3}\right)$, where $\|h^{\star}\|_{\mathsf{sp}}$ is the span norm of the bias function, improving previous results by at least a factor of $\frac{\|h^{\star}\|_{\mathsf{sp}}^2}{\varepsilon^2}$. In the federated setting with $M$ agents, we prove that collaboration reduces the per-agent sample complexity to $\widetilde{O}\left(\frac{|\mathcal{S}||\mathcal{A}|\|h^{\star}\|_{\mathsf{sp}}^3}{M\varepsilon^3}\right)$, with only $\widetilde{O}\left(\frac{\|h^{\star}\|_{\mathsf{sp}}}{\varepsilon}\right)$ communication rounds required. These results establish the first federated Q-learning algorithm for average-reward MDPs, with provable efficiency in both sample and communication complexity.

This paper develops a novel and unified framework to analyze the convergence of a large family of Q-learning algorithms from the switching system perspective. We show that the nonlinear ODE models associated with Q-learning and many of its variants can be naturally formulated as affine switching systems. Building on their asymptotic stability, we obtain a number of interesting results: (i) we provide a simple ODE analysis for the convergence of asynchronous Q-learning under relatively weak assumptions; (ii) we establish the first convergence analysis of the averaging Q-learning algorithm; and (iii) we derive a new sufficient condition for the convergence of Q-learning with linear function approximation.