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Federated Learning (FL) refers to distributed protocols that avoid direct rawdata exchange among the participating devices while training for a commonlearning task. This way, FL can potentially reduce the information on the localdata sets that is leaked via communications. In order to provide formal privacyguarantees, however, it is generally necessary to put in place additionalmasking mechanisms. When FL is implemented in wireless systems via uncodedtransmission, the channel noise can directly act as a privacy-inducingmechanism. This paper demonstrates that, as long as the privacy constraintlevel, measured via differential privacy (DP), is below a threshold thatdecreases with the signal-to-noise ratio (SNR), uncoded transmission achievesprivacy "for free", i.e., without affecting the learning performance. Moregenerally, this work studies adaptive power allocation (PA) for decentralizedgradient descent in wireless FL with the aim of minimizing the learningoptimality gap under privacy and power constraints. Both orthogonal multipleaccess (OMA) and non-orthogonal multiple access (NOMA) transmission with"over-the-air-computing" are studied, and solutions are obtained in closed formfor an offline optimization setting. Furthermore, heuristic online methods areproposed that leverage iterative one-step-ahead optimization. The importance ofdynamic PA and the potential benefits of NOMA versus OMA are demonstratedthrough extensive simulations.

Privacy For Free: Wireless Federated Learning Via Uncoded Transmission With Adaptive Power Control