Provably Efficient Federated Reinforcement Learning with Linear Function Approximation and Logarithmic Communication Cost
Zihang Liang, Haochen Zhang, Lingzhou Xue
Abstract
We study federated online reinforcement learning with linear function approximation. While recent multi-agent reinforcement learning algorithms achieve strong regret guarantees, they typically require sharing raw trajectories. This reliance incurs a communication cost that scales linearly with the number of episodes and violates the privacy constraints of federated settings. To address these limitations, we propose Fed-LSVI, the first provably efficient federated algorithm for online reinforcement learning with linear function approximation in episodic Markov decision processes. By integrating a determinant-based event-triggered synchronization with a stepwise backward update mechanism, Fed-LSVI enables agents to collaboratively learn an optimal policy by exchanging only compressed sufficient statistics. We prove that Fed-LSVI achieves a regret bound of $\widetilde{\mathcal O}(\sqrt{Md^3H^4T})$, where $d$ is the feature dimension, $H$ is the horizon length, $M$ is the number of agents, and $T$ is the number of episodes per agent, matching the best-known regret for multi-agent online reinforcement learning with linear function approximation. Moreover, by following the stringent communication and privacy constraints of the federated setting, Fed-LSVI reduces the communication cost to only logarithmic dependence on $T$, representing a significant improvement over prior methods.