  Federated learning has generated significant interest, with nearly all works
focused on a "star" topology where nodes/devices are each connected to a
central server. We migrate away from this architecture and extend it through
the network dimension to the case where there are multiple layers of nodes
between the end devices and the server. Specifically, we develop multi-stage
hybrid federated learning (MH-FL), a hybrid of intra- and inter-layer model
learning that considers the network as a multi-layer cluster-based structure.
MH-FL considers the topology structures among the nodes in the clusters,
including local networks formed via device-to-device (D2D) communications, and
presumes a semi-decentralized architecture for federated learning. It
orchestrates the devices at different network layers in a
collaborative/cooperative manner (i.e., using D2D interactions) to form local
consensus on the model parameters and combines it with multi-stage parameter
relaying between layers of the tree-shaped hierarchy. We derive the upper bound
of convergence for MH-FL with respect to parameters of the network topology
(e.g., the spectral radius) and the learning algorithm (e.g., the number of D2D
rounds in different clusters). We obtain a set of policies for the D2D rounds
at different clusters to guarantee either a finite optimality gap or
convergence to the global optimum. We then develop a distributed control
algorithm for MH-FL to tune the D2D rounds in each cluster over time to meet
specific convergence criteria. Our experiments on real-world datasets verify
our analytical results and demonstrate the advantages of MH-FL in terms of
resource utilization metrics.
