On the Convergence of Hierarchical Federated Learning with Gradient Quantization and Imperfect Transmission

To enhance the robustness and convergence of hierarchical federated learning (HFL) in wireless networks with imperfect channel state information (CSI), a quantized HFL (QHFL) framework is proposed. Considering the local training and communication latency, the outage probability of quantized gradient transmission is modeled under imperfect CSI. Then, the convergence of the proposed QHFL with transmission outage and gradient quantization is analyzed. Simulation results demonstrate the correlation between quantization accuracy and transmission outage, along with their joint impact on the HFL convergence, which align with the insight behind the convergence analysis.