  Online federated learning (FL) enables geographically distributed devices to
learn a global shared model from locally available streaming data. Most online
FL literature considers a best-case scenario regarding the participating
clients and the communication channels. However, these assumptions are often
not met in real-world applications. Asynchronous settings can reflect a more
realistic environment, such as heterogeneous client participation due to
available computational power and battery constraints, as well as delays caused
by communication channels or straggler devices. Further, in most applications,
energy efficiency must be taken into consideration. Using the principles of
partial-sharing-based communications, we propose a communication-efficient
asynchronous online federated learning (PAO-Fed) strategy. By reducing the
communication overhead of the participants, the proposed method renders
participation in the learning task more accessible and efficient. In addition,
the proposed aggregation mechanism accounts for random participation, handles
delayed updates and mitigates their effect on accuracy. We prove the first and
second-order convergence of the proposed PAO-Fed method and obtain an
expression for its steady-state mean square deviation. Finally, we conduct
comprehensive simulations to study the performance of the proposed method on
both synthetic and real-life datasets. The simulations reveal that in
asynchronous settings, the proposed PAO-Fed is able to achieve the same
convergence properties as that of the online federated stochastic gradient
while reducing the communication overhead by 98 percent.
