In this paper, we study the problem of federated learning over a wireless channel with user sampling, modeled by a fading multiple access channel, subject to central and local differential privacy (DP/LDP) constraints. It has been shown that the superposition nature of the wireless channel provides a dual benefit of bandwidth efficient gradient aggregation, in conjunction with strong DP guarantees for the users. Specifically, the central DP privacy leakage has been shown to scale as $\mathcal {O}(1/K^{1/2})$ , where $K$ is the number of users. It has also been shown that user sampling coupled with orthogonal transmission can enhance the central DP privacy leakage with the same scaling behavior. In this work, we show that, by jointly incorporating both wireless aggregation and user sampling, one can obtain even stronger privacy guarantees. We propose a private wireless gradient aggregation scheme, which relies on independently randomized participation decisions by each user. The central 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 present analysis for the convergence rate of the proposed scheme and study the tradeoffs between wireless resources, convergence, and privacy theoretically and empirically for two scenarios when the number of sampled participants are $(a)$ known, or $(b)$ unknown at the parameter server.

中文翻译：

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通过用户采样和无线聚合增强联邦学习的隐私


在本文中，我们研究了具有用户采样的无线信道上的联邦学习问题，该问题通过衰落多址信道建模，并受到中央和本地差分隐私（DP/LDP）约束。事实证明，无线信道的叠加性质提供了带宽高效梯度聚合的双重好处，同时为用户提供了强大的 DP 保证。具体来说，中心 DP 隐私泄漏已被证明按 $\mathcal {O}(1/K^{1/2})$ 缩放，其中 $K$ 是用户数量。研究还表明，用户采样与正交传输相结合可以在相同的缩放行为下增强中央 DP 隐私泄漏。在这项工作中，我们表明，通过联合结合无线聚合和用户采样，可以获得更强的隐私保证。我们提出了一种私有无线梯度聚合方案，该方案依赖于每个用户独立随机的参与决策。我们提出的方案的中心 DP 泄漏缩放为 $\mathcal {O}(1/K^{3/4})$ 。此外，我们还表明 LDP 也受到用户抽样的推动。我们还对所提出方案的收敛速度进行了分析，并从理论上和实证上研究了当样本参与者数量已知 $(a)​​$ 或 $(b)$ 时的两种情况下无线资源、收敛和隐私之间的权衡在参数服务器上未知。