  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.
