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In this paper, we study the problem of federated learning over a wirelesschannel with user sampling, modeled by a Gaussian multiple access channel,subject to central and local differential privacy (DP/LDP) constraints. It hasbeen shown that the superposition nature of the wireless channel provides adual benefit of bandwidth efficient gradient aggregation, in conjunction withstrong DP guarantees for the users. Specifically, the central DP privacyleakage has been shown to scale as $\mathcal{O}(1/K^{1/2})$, where $K$ is thenumber of users. It has also been shown that user sampling coupled withorthogonal transmission can enhance the central DP privacy leakage with thesame scaling behavior. In this work, we show that, by join incorporating bothwireless aggregation and user sampling, one can obtain even stronger privacyguarantees. We propose a private wireless gradient aggregation scheme, whichrelies on independently randomized participation decisions by each user. Thecentral DP leakage of our proposed scheme scales as $\mathcal{O}(1/K^{3/4})$.In addition, we show that LDP is also boosted by user sampling. We also presentanalysis for the convergence rate of the proposed scheme and study thetradeoffs between wireless resources, convergence, and privacy theoreticallyand empirically for two scenarios when the number of sampled participants are$(a)$ known, or $(b)$ unknown at the parameter server.

Privacy Amplification for Federated Learning via User Sampling and Wireless Aggregation