Personalized Observation Normalization for Federated Reinforcement Learning in Simulation Environments with Heterogeneity

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 variant, bound its bias, and exhibit fixed points at which the meta-gradient is nonzero and of order $α$, showing that the resulting stationarity floor is a property of the method rather than of the bound. Experiments on tabular and neural navigation confirm the predicted behavior and show transfer to unseen agents at an order of magnitude lower sample cost than independent training. Together these results identify the adaptation step size as a tunable personalization knob and the curvature estimate as the quantity that governs whether exact meta-gradients are affordable.

Federated Reinforcement Learning (FRL) enables collaborative policy learning across distributed agents with heterogeneous environments. While recent methods based on variance reduction, divergence penalization, and momentum optimization improve FRL under heterogeneous settings, they still primarily synchronize policy or value-network parameters and do not explicitly address distributional mismatch among heterogeneous clients. Therefore, we propose FedGuide, a FRL framework that uses diffusion priors as behavior models to provide personalized data supported distributions for heterogeneous local policy learning. Instead of directly averaging local policies, FedGuide aggregates those diffusion priors through Optimal-Transport Mixture-of-Experts (OT-MoE), preserving heterogeneous behavior modes in distribution space. It further develops a Distribution Correction Estimation (DICE) value baseline to provide low-variance, return-aware guidance for local policy improvement. Experiments across heterogeneous environments show that FedGuide outperforms representative FRL methods in client-average returns, final-round performance, and worst-round robustness, while maintaining stable learning under stronger heterogeneity.

This paper considers reinforcement learning from human feedback in a federated learning setting with resource-constrained agents, such as edge devices. We propose an efficient federated RLHF algorithm, named Partitioned, Sign-based Stochastic Zeroth-order Policy Optimization (Par-S$^2$ZPO). The algorithm is built on zeroth-order optimization with binary perturbation, resulting in low communication, computation, and memory complexity by design. Our theoretical analysis establishes an upper bound on the convergence rate of Par-S$^2$ZPO, revealing that it is as efficient as its centralized counterpart in terms of sample complexity but converges faster in terms of policy update iterations. Our experimental results show that it outperforms a FedAvg-based RLHF on four MuJoCo RL tasks.