  This paper studies issues that arise with respect to the joint optimization
for convergence time in federated learning over wireless networks (FLOWN). We
consider the criterion and protocol for selection of participating devices in
FLOWN under the energy constraint and derive its impact on device selection. In
order to improve the training efficiency, age-of-information (AoI) enables
FLOWN to assess the freshness of gradient updates among participants. Aiming to
speed up convergence, we jointly investigate global loss minimization and
latency minimization in a Stackelberg game based framework. Specifically, we
formulate global loss minimization as a leader-level problem for reducing the
number of required rounds, and latency minimization as a follower-level problem
to reduce time consumption of each round. By decoupling the follower-level
problem into two sub-problems, including resource allocation and sub-channel
assignment, we achieve an optimal strategy of the follower through monotonic
optimization and matching theory. At the leader-level, we derive an upper bound
of convergence rate and subsequently reformulate the global loss minimization
problem and propose a new age-of-update (AoU) based device selection algorithm.
Simulation results indicate the superior performance of the proposed AoU based
device selection scheme in terms of the convergence rate, as well as efficient
utilization of available sub-channels.
