  With the development of federated learning (FL), mobile devices (MDs) are
able to train their local models with private data and sends them to a central
server for aggregation, thereby preventing sensitive raw data leakage. In this
paper, we aim to improve the training performance of FL systems in the context
of wireless channels and stochastic energy arrivals of MDs. To this purpose, we
dynamically optimize MDs' transmission power and training task scheduling. We
first model this dynamic programming problem as a constrained Markov decision
process (CMDP). Due to high dimensions rooted from our CMDP problem, we propose
online stochastic learning methods to simplify the CMDP and design online
algorithms to obtain an efficient policy for all MDs. Since there are long-term
constraints in our CMDP, we utilize Lagrange multipliers approach to tackle
this issue. Furthermore, we prove the convergence of the proposed online
stochastic learning algorithm. Numerical results indicate that the proposed
algorithms can achieve better performance than the benchmark algorithms.
