stat.MLAug 31, 2026

Provably Efficient Federated Reinforcement Learning with Linear Function Approximation and Logarithmic Communication Cost

Authors: Zihang LiangHaochen ZhangLingzhou Xue

Organizations: Department of Statistics, The Pennsylvania State University

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 O~(Md3H4T)\widetilde{\mathcal O}(\sqrt{Md^3H^4T}), where dd is the feature dimension, HH is the horizon length, MM is the number of agents, and TT 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 TT, representing a significant improvement over prior methods.

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