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Federated Learning (FL), an emerging paradigm for fast intelligentacquisition at the network edge, enables joint training of a machine learningmodel over distributed data sets and computing resources with limiteddisclosure of local data. Communication is a critical enabler of large-scale FLdue to significant amount of model information exchanged among edge devices. Inthis paper, we consider a network of wireless devices sharing a common fadingwireless channel for the deployment of FL. Each device holds a generallydistinct training set, and communication typically takes place in aDevice-to-Device (D2D) manner. In the ideal case in which all devices withincommunication range can communicate simultaneously and noiselessly, a standardprotocol that is guaranteed to converge to an optimal solution of the globalempirical risk minimization problem under convexity and connectivityassumptions is Decentralized Stochastic Gradient Descent (DSGD). DSGDintegrates local SGD steps with periodic consensus averages that requirecommunication between neighboring devices. In this paper, wireless protocolsare proposed that implement DSGD by accounting for the presence of path loss,fading, blockages, and mutual interference. The proposed protocols are based ongraph coloring for scheduling and on both digital and analog transmissionstrategies at the physical layer, with the latter leveraging over-the-aircomputing via sparsity-based recovery.

Decentralized Federated Learning via SGD over Wireless D2D Networks