In this letter, we introduce over-the-air computation into the communication design of federated multi-task learning (FMTL), and propose an over-the-air federated multi-task learning (OA-FMTL) framework, where multiple learning tasks deployed on edge devices share a non-orthogonal fading channel under the coordination of an edge server (ES). Specifically, the model updates for all the tasks are transmitted and superimposed concurrently over a non-orthogonal uplink fading channel, and the model aggregations of all the tasks are reconstructed at the ES through a modified version of the turbo compressed sensing algorithm (Turbo-CS) that overcomes inter-task interference. Both convergence analysis and numerical results show that the OA-FMTL framework can significantly improve the system efficiency in terms of reducing the number of channel uses without causing substantial learning performance degradation.
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