1-Bit Compressive Sensing for Efficient Federated Learning Over the Air

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For distributed learning among collaborative users, this paper develops and analyzes a communication-efficient scheme for federated learning (FL) over the air, which incorporates 1-bit compressive sensing (CS) into analog aggregation transmissions.

• To facilitate design parameter optimization, we theoretically analyze the efficacy of the proposed scheme by deriving a closed-form expression for the expected convergence rate of the FL over the air.
• Our theoretical results reveal the tradeoff between convergence performance and communication efficiency as a result of the aggregation errors caused by sparsification, dimension reduction, quantization, signal reconstruction and noise.
• Then, we formulate 1-bit CS based FL over the air as a joint optimization problem to mitigate the impact of these aggregation errors through joint optimal design of worker scheduling and power scaling policy.