Dynamic Clustering and Power Control for Two-Tier Over-the-Air Federated Learning

Federated learning (FL) has been recognized as a promising distributed learning paradigm to support intelligent applications at the wireless edge. However, direct computing based on the information from the devices may not be resource efficient due to the relatively large communication cost between the devices and parameter server (PS). This paper studies the joint communication and learning design for the over-theair computation (AirComp)-based two-tier wireless FL scheme, where the lead devices first collect the local gradients from their nearby subordinate devices, and then send the merged results to the PS for the second round of aggregation. We establish a convergence result for the proposed scheme and derive the upper bound on the optimality gap between the expected and optimal global loss values. Next, based on the device distance and data importance, we propose a hierarchical clustering method to build the two-tier structure. Then, with only the instantaneous channel state information (CSI), we formulate the optimality gap minimization problem and solve it by using an efficient alternating minimization method. Numerical results show that the proposed scheme outperforms the baseline ones.