  Federated reinforcement learning (FedRL) enables agents to collaboratively
train a global policy without sharing their individual data. However, high
communication overhead remains a critical bottleneck, particularly for natural
policy gradient (NPG) methods, which are second-order. To address this issue,
we propose the FedNPG-ADMM framework, which leverages the alternating direction
method of multipliers (ADMM) to approximate global NPG directions efficiently.
We theoretically demonstrate that using ADMM-based gradient updates reduces
communication complexity from ${O}({d^{2}})$ to ${O}({d})$ at each iteration,
where $d$ is the number of model parameters. Furthermore, we show that
achieving an $\epsilon$-error stationary convergence requires
${O}(\frac{1}{(1-\gamma)^{2}{\epsilon}})$ iterations for discount factor
$\gamma$, demonstrating that FedNPG-ADMM maintains the same convergence rate as
the standard FedNPG. Through evaluation of the proposed algorithms in MuJoCo
environments, we demonstrate that FedNPG-ADMM maintains the reward performance
of standard FedNPG, and that its convergence rate improves when the number of
federated agents increases.
