Sample Complexity of Average-Reward Q-Learning: From Single-agent to Federated Reinforcement Learning

• URL: http://arxiv.org/abs/2601.13642v1
• Date: Tue, 20 Jan 2026 06:21:54 GMT
• Title: Sample Complexity of Average-Reward Q-Learning: From Single-agent to Federated Reinforcement Learning
• Authors: Yuchen Jiao, Jiin Woo, Gen Li, Gauri Joshi, Yuejie Chi,
• Abstract summary: We study a simple but effective Q-learning algorithm for average-reward MDPs with finite state and action spaces under the weakly communicating assumption.<n>We prove that collaboration reduces the per-agent sample complexity to $widetildeOleft(frac|mathcalA||hstar|_mathsfsp3Mvarepsilon3right)$, with only $widetildeOleft(frac|hstar|_mathsfsp3Mvareps
• Score: 51.820005667020354
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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