  In this paper, we study asynchronous federated learning (FL) in a wireless
distributed learning network (WDLN). To allow each edge device to use its local
data more efficiently via asynchronous FL, transmission scheduling in the WDLN
for asynchronous FL should be carefully determined considering system
uncertainties, such as time-varying channel and stochastic data arrivals, and
the scarce radio resources in the WDLN. To address this, we propose a metric,
called an effectivity score, which represents the amount of learning from
asynchronous FL. We then formulate an Asynchronous Learning-aware transmission
Scheduling (ALS) problem to maximize the effectivity score and develop three
ALS algorithms, called ALSA-PI, BALSA, and BALSA-PO, to solve it. If the
statistical information about the uncertainties is known, the problem can be
optimally and efficiently solved by ALSA-PI. Even if not, it can be still
optimally solved by BALSA that learns the uncertainties based on a Bayesian
approach using the state information reported from devices. BALSA-PO
suboptimally solves the problem, but it addresses a more restrictive WDLN in
practice, where the AP can observe a limited state information compared with
the information used in BALSA. We show via simulations that the models trained
by our ALS algorithms achieve performances close to that by an ideal benchmark
and outperform those by other state-of-the-art baseline scheduling algorithms
in terms of model accuracy, training loss, learning speed, and robustness of
learning. These results demonstrate that the adaptive scheduling strategy in
our ALS algorithms is effective to asynchronous FL.
