Adaptive Beam Hopping for Over-the-Air Online Federated Learning in LEO Satellite Networks

This paper investigates over-the-air (OTA) computation federated learning (FL) in low-earth orbit (LEO) satellite networks, where we propose a novel joint design of adaptive beam hopping and power control to maximize the long-term total amount of training data. This problem is challenging due to the non-convex coupling between beam hopping patterns, power control, and global mean squared error (MSE) constraints, as well as the dynamic satellite coverage. To address these difficulties, we develop a proximal policy optimization (PPO)-based deep reinforcement learning framework that learns efficient scheduling policies. In particular, the proposed method jointly optimizes beam hopping patterns and transmission power, while incorporating MSE-aware reward shaping to balance data utilization and aggregation accuracy. Simulation results demonstrate that the proposed PPO approach achieves faster convergence, higher reward, and superior FL performance in terms of test accuracy and training loss, compared with soft actor-critic (SAC), deep deterministic policy gradient (DDPG), and a greedy baseline.