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Federated learning (FL) encounters scalability challenges when implementedover fog networks. Semi-decentralized FL (SD-FL) proposes a solution thatdivides model cooperation into two stages: at the lower stage, device-to-device(D2D) communications is employed for local model aggregations withinsubnetworks (subnets), while the upper stage handles device-server (DS)communications for global model aggregations. However, existing SD-FL schemesare based on gradient diversity assumptions that become performance bottlenecksas data distributions become more heterogeneous. In this work, we developsemi-decentralized gradient tracking (SD-GT), the first SD-FL methodology thatremoves the need for such assumptions by incorporating tracking terms intodevice updates for each communication layer. Analytical characterization ofSD-GT reveals convergence upper bounds for both non-convex and strongly-convexproblems, for a suitable choice of step size. We employ the resulting bounds inthe development of a co-optimization algorithm for optimizing subnet samplingrates and D2D rounds according to a performance-efficiency trade-off. Oursubsequent numerical evaluations demonstrate that SD-GT obtains substantialimprovements in trained model quality and communication cost relative tobaselines in SD-FL and gradient tracking on several datasets.

Taming Subnet-Drift in D2D-Enabled Fog Learning: A Hierarchical Gradient Tracking Approach