  Federated Learning (FL), an emerging paradigm for fast intelligent
acquisition at the network edge, enables joint training of a machine learning
model over distributed data sets and computing resources with limited
disclosure of local data. Communication is a critical enabler of large-scale FL
due to significant amount of model information exchanged among edge devices. In
this paper, we consider a network of wireless devices sharing a common fading
wireless channel for the deployment of FL. Each device holds a generally
distinct training set, and communication typically takes place in a
Device-to-Device (D2D) manner. In the ideal case in which all devices within
communication range can communicate simultaneously and noiselessly, a standard
protocol that is guaranteed to converge to an optimal solution of the global
empirical risk minimization problem under convexity and connectivity
assumptions is Decentralized Stochastic Gradient Descent (DSGD). DSGD
integrates local SGD steps with periodic consensus averages that require
communication between neighboring devices. In this paper, wireless protocols
are proposed that implement DSGD by accounting for the presence of path loss,
fading, blockages, and mutual interference. The proposed protocols are based on
graph coloring for scheduling and on both digital and analog transmission
strategies at the physical layer, with the latter leveraging over-the-air
computing via sparsity-based recovery.
