  Federated learning has emerged as a popular technique for distributing model
training across the network edge. Its learning architecture is conventionally a
star topology between the devices and a central server. In this paper, we
propose two timescale hybrid federated learning (TT-HF), which migrates to a
more distributed topology via device-to-device (D2D) communications. In TT-HF,
local model training occurs at devices via successive gradient iterations, and
the synchronization process occurs at two timescales: (i) macro-scale, where
global aggregations are carried out via device-server interactions, and (ii)
micro-scale, where local aggregations are carried out via D2D cooperative
consensus formation in different device clusters. Our theoretical analysis
reveals how device, cluster, and network-level parameters affect the
convergence of TT-HF, and leads to a set of conditions under which a
convergence rate of O(1/t) is guaranteed. Experimental results demonstrate the
improvements in convergence and utilization that can be obtained by TT-HF over
state-of-the-art federated learning baselines.
