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

arXiv:2609.00193v1 Announce Type: cross 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.

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.

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

arXiv:2609.00193 [stat.ML]

(or arXiv:2609.00193v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2609.00193 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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

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