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Semi-decentralized federated learning blends the conventional deviceto-server (D2S) interaction structure of federated model training withlocalized device-to-device (D2D) communications. We study this architectureover practical edge networks with multiple D2D clusters modeled as time-varyingand directed communication graphs. Our investigation results in an algorithmthat controls the fundamental trade-off between (a) the rate of convergence ofthe model training process towards the global optimizer, and (b) the number ofD2S transmissions required for global aggregation. Specifically, in oursemi-decentralized methodology, D2D consensus updates are injected into thefederated averaging framework based on column-stochastic weight matrices thatencapsulate the connectivity within the clusters. To arrive at our algorithm,we show how the expected optimality gap in the current global model depends onthe greatest two singular values of the weighted adjacency matrices (and henceon the densities) of the D2D clusters. We then derive tight bounds on thesesingular values in terms of the node degrees of the D2D clusters, and we usethe resulting expressions to design a threshold on the number of clientsrequired to participate in any given global aggregation round so as to ensure adesired convergence rate. Simulations performed on real-world datasets revealthat our connectivity-aware algorithm reduces the total communication costrequired to reach a target accuracy significantly compared with baselinesdepending on the connectivity structure and the learning task.

Connectivity-Aware Semi-Decentralized Federated Learning over Time-Varying D2D Networks