Over-the-Air Multi-Task Federated Learning Over MIMO Interference Channel

With the explosive growth of data and wireless devices, federated learning (FL) has emerged as a promising technology for large-scale intelligent systems. Utilizing the analog superposition of electromagnetic waves, over-the-air computation is an appealing approach to reduce the burden of communication in the FL model aggregation. However, with the urgent demand for intelligent systems, the training of multiple tasks with over-the-air computation further aggravates the scarcity of communication resources. This issue can be alleviated to some extent by training multiple tasks simultaneously with shared communication resources, but the latter inevitably brings about the problem of inter-task interference. In this paper, we study over-the-air multi-task FL (OA-MTFL) over the multiple-input multiple-output (MIMO) interference channel. We propose a novel model aggregation method for the alignment of local gradients for different devices, which alleviates the straggler problem that exists widely in over-the-air computation due to the channel heterogeneity. We establish a unified communication-computation analysis framework for the proposed OA-MTFL scheme by considering the spatial correlation between devices, and formulate an optimization problem of designing transceiver beamforming and device selection. We develop an algorithm by using alternating optimization (AO) and fractional programming (FP) to solve this problem, which effectively relieves the impact of inter-task interference on the FL learning performance. We show that due to the use of the new model aggregation method, device selection is no longer essential to our scheme, thereby avoiding the heavy computational burden caused by implementing device selection. The numerical results demonstrate the correctness of the analysis and the outstanding performance of the proposed scheme.