  Federated learning (FL) has emerged as an instance of distributed machine
learning paradigm that avoids the transmission of data generated on the users'
side. Although data are not transmitted, edge devices have to deal with limited
communication bandwidths, data heterogeneity, and straggler effects due to the
limited computational resources of users' devices. A prominent approach to
overcome such difficulties is FedADMM, which is based on the classical
two-operator consensus alternating direction method of multipliers (ADMM). The
common assumption of FL algorithms, including FedADMM, is that they learn a
global model using data only on the users' side and not on the edge server.
However, in edge learning, the server is expected to be near the base station
and have direct access to rich datasets. In this paper, we argue that
leveraging the rich data on the edge server is much more beneficial than
utilizing only user datasets. Specifically, we show that the mere application
of FL with an additional virtual user node representing the data on the edge
server is inefficient. We propose FedTOP-ADMM, which generalizes FedADMM and is
based on a three-operator ADMM-type technique that exploits a smooth cost
function on the edge server to learn a global model parallel to the edge
devices. Our numerical experiments indicate that FedTOP-ADMM has substantial
gain up to 33\% in communication efficiency to reach a desired test accuracy
with respect to FedADMM, including a virtual user on the edge server.
