  A recent emphasis of distributed learning research has been on federated
learning (FL), in which model training is conducted by the data-collecting
devices. Existing research on FL has mostly focused on a star topology learning
architecture with synchronized (time-triggered) model training rounds, where
the local models of the devices are periodically aggregated by a centralized
coordinating node. However, in many settings, such a coordinating node may not
exist, motivating efforts to fully decentralize FL. In this work, we propose a
novel methodology for distributed model aggregations via asynchronous,
event-triggered consensus iterations over the network graph topology. We
consider heterogeneous communication event thresholds at each device that weigh
the change in local model parameters against the available local resources in
deciding the benefit of aggregations at each iteration. Through theoretical
analysis, we demonstrate that our methodology achieves asymptotic convergence
to the globally optimal learning model under standard assumptions in
distributed learning and graph consensus literature, and without restrictive
connectivity requirements on the underlying topology. Subsequent numerical
results demonstrate that our methodology obtains substantial improvements in
communication requirements compared with FL baselines.
