  Energy is an essential, but often forgotten aspect in large-scale federated
systems. As most of the research focuses on tackling computational and
statistical heterogeneity from the machine learning algorithms, the impact on
the mobile system still remains unclear. In this paper, we design and implement
an online optimization framework by connecting asynchronous execution of
federated training with application co-running to minimize energy consumption
on battery-powered mobile devices. From a series of experiments, we find that
co-running the training process in the background with foreground applications
gives the system a deep energy discount with negligible performance slowdown.
Based on these results, we first study an offline problem assuming all the
future occurrences of applications are available, and propose a dynamic
programming-based algorithm. Then we propose an online algorithm using the
Lyapunov framework to explore the solution space via the energy-staleness
trade-off. The extensive experiments demonstrate that the online optimization
framework can save over 60% energy with 3 times faster convergence speed
compared to the previous schemes.
