  Federated learning (FL) requires edge devices to perform local training and
exchange information with a parameter server, leading to substantial energy
consumption. A critical challenge in practical FL systems is the rapid energy
depletion of battery-limited edge devices, which curtails their operational
lifespan and affects the learning performance. To address this issue, we apply
energy harvesting technique in FL systems to extract ambient energy for
continuously powering edge devices. We first establish the convergence bound
for the wireless FL system with energy harvesting devices, illustrating that
the convergence is impacted by partial device participation and packet drops,
both of which depend on the energy supply. To accelerate the convergence, we
formulate a joint device scheduling and power control problem and model it as a
Markov decision process (MDP). By solving this MDP, we derive the optimal
transmission policy and demonstrate that it possesses a monotone structure with
respect to the battery and channel states. To overcome the curse of
dimensionality caused by the exponential complexity of computing the optimal
policy, we propose a low-complexity algorithm, which is asymptotically optimal
as the number of devices increases. Furthermore, for unknown channels and
harvested energy statistics, we develop a structure-enhanced deep reinforcement
learning algorithm that leverages the monotone structure of the optimal policy
to improve the training performance. Finally, extensive numerical experiments
on real-world datasets are presented to validate the theoretical results and
corroborate the effectiveness of the proposed algorithms.
