Over-the-Air Federated Multi-Task Learning Over MIMO Multiple Access Channels

With the explosive growth of data and wireless devices, federated learning (FL) over wireless medium has emerged as a promising technology for large-scale distributed intelligent systems. Yet, the urgent demand for ubiquitous intelligence will generate a large number of concurrent FL tasks, which may seriously aggravate the scarcity of communication resources. By exploiting the analog superposition of electromagnetic waves, over-the-air computation (AirComp) is an appealing solution to alleviate the burden of communication required by FL. However, sharing frequency-time resources in over-the-air computation inevitably brings about the problem of inter-task interference, which poses a new challenge that needs to be appropriately addressed. In this paper, we study over-the-air federated multi-task learning (OA-FMTL) over the multiple-input multiple-output (MIMO) multiple access (MAC) channel. We propose a novel model aggregation method for the alignment of local gradients of different devices, which alleviates the straggler problem in over-the-air computation due to the channel heterogeneity. We establish a communication-learning analysis framework for the proposed OA-FMTL scheme by considering the spatial correlation between devices, and formulate an optimization problem for the design of transceiver beamforming and device selection. To solve this problem, we develop an algorithm by using alternating optimization (AO) and fractional programming (FP), which effectively mitigates 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, thereby avoiding the heavy computational burden involved in selecting active devices. Numerical results demonstrate the validity of the analysis and the superb performance of the proposed scheme.