  Asynchronous federated learning aims to solve the straggler problem in
heterogeneous environments, i.e., clients have small computational capacities
that could cause aggregation delay. The principle of asynchronous federated
learning is to allow the server to aggregate the model once it receives an
update from any client rather than waiting for updates from multiple clients or
waiting a specified amount of time in the synchronous mode. Due to the
asynchronous setting, the stale model problem could occur, where the slow
clients could utilize an outdated local model for their local data training.
Consequently, when these locally trained models are uploaded to the server,
they may impede the convergence of the global training. Therefore, effective
model aggregation strategies play a significant role in updating the global
model. Besides, client scheduling is also critical when heterogeneous clients
with diversified computing capacities are participating in the federated
learning process. This work first investigates the impact of the convergence of
asynchronous federated learning mode when adopting the aggregation coefficient
in synchronous mode. The effective aggregation solutions that can achieve the
same convergence result as in the synchronous mode are then proposed, followed
by an improved aggregation method with client scheduling. The simulation
results in various scenarios demonstrate that the proposed algorithm converges
with a similar level of accuracy as the classical synchronous federated
learning algorithm but effectively accelerates the learning process, especially
in its early stage.
