  Recent advances in machine learning, wireless communication, and mobile
hardware technologies promisingly enable federated learning (FL) over massive
mobile edge devices, which opens new horizons for numerous intelligent mobile
applications. Despite the potential benefits, FL imposes huge communication and
computation burdens on participating devices due to periodical global
synchronization and continuous local training, raising great challenges to
battery constrained mobile devices. In this work, we target at improving the
energy efficiency of FL over mobile edge networks to accommodate heterogeneous
participating devices without sacrificing the learning performance. To this
end, we develop a convergence-guaranteed FL algorithm enabling flexible
communication compression. Guided by the derived convergence bound, we design a
compression control scheme to balance the energy consumption of local computing
(i.e., "working") and wireless communication (i.e., "talking") from the
long-term learning perspective. In particular, the compression parameters are
elaborately chosen for FL participants adapting to their computing and
communication environments. Extensive simulations are conducted using various
datasets to validate our theoretical analysis, and the results also demonstrate
the efficacy of the proposed scheme in energy saving.
