Hierarchical Federated Learning Across Heterogeneous Cellular Networks

Our proposed HFL framework consists of 4 communication steps: uplink from MU to SBS, downlink from SBS to MU, uplink from SBS to MBS and downlink from MBS to SBS. For each communication step, we employ different sparsification parameters, ϕulMU, ϕdlSBS, ϕulSBS and ϕdlMBS respectively, to speed up the communication. We introduce the function Ω(V,ϕ):Rd Rd, which maps a d dimensional vector to its sparse form where only 1 ϕ portion of the indicies have non-zero values. The sparsification procedure in each step leads to an error in the parameter model and thus slows down the convergence. To overcome this issue we employ the discounted error accumulation technique, similar to [SGD_q4, fedlearn7], which uses the discounted version of the error for the next model update.