  Federated learning (FL) is a technique for distributed machine learning (ML),
in which edge devices carry out local model training on their individual
datasets. In traditional FL algorithms, trained models at the edge are
periodically sent to a central server for aggregation, utilizing a star
topology as the underlying communication graph. However, assuming access to a
central coordinator is not always practical, e.g., in ad hoc wireless network
settings. In this paper, we develop a novel methodology for fully decentralized
FL, where in addition to local training, devices conduct model aggregation via
cooperative consensus formation with their one-hop neighbors over the
decentralized underlying physical network. We further eliminate the need for a
timing coordinator by introducing asynchronous, event-triggered communications
among the devices. In doing so, to account for the inherent resource
heterogeneity challenges in FL, we define personalized communication triggering
conditions at each device that weigh the change in local model parameters
against the available local resources. We theoretically demonstrate that our
methodology converges to the globally optimal learning model at a
$O{(\frac{\ln{k}}{\sqrt{k}})}$ rate under standard assumptions in distributed
learning and consensus literature. Our subsequent numerical evaluations
demonstrate that our methodology obtains substantial improvements in
convergence speed and/or communication savings compared with existing
decentralized FL baselines.
