Personalized Federated Reinforcement Learning via Model-Agnostic Meta-Learning: Convergence of Exact and Hessian-Free Meta-Policy Gradients

Ali Beikmohammadi, Sarit Khirirat, Sindri Magnússon

We study personalized federated reinforcement learning, in which $n$ agents, each acting in its own Markov decision process, collaborate through a server to learn a shared MAML-style policy initialization that becomes effective for an individual agent once that agent adapts it with a single local policy-gradient step. We propose Per-FedAvg-PG, in which agents take $τ$ local stochastic meta-policy-gradient steps between communication rounds, and prove that it reaches an $\varepsilon$-approximate first-order stationary point of the personalized objective in $K=\mathcal O(\varepsilon^{-3/2})$ rounds with $τ=Θ(\varepsilon^{-1/2})$ local steps. The analysis rests on a structural feature of the reinforcement learning setting: under standard policy-class regularity, the per-agent objectives have uniformly bounded gradients and Hessians with explicit constants, so the bounded-gradient and bounded-heterogeneity conditions imposed by the supervised theory hold automatically and no separate heterogeneity assumption is needed. The exact meta-gradient requires the inner-loop policy Hessian, which our experiments identify as the practical bottleneck. We therefore analyze the Hessian-free…