Federated Learning (FL) refers to distributed protocols that avoid direct raw data exchange among the participating devices while training for a common learning task. This way, FL can potentially reduce the information on the local data sets that is leaked via communications. In order to provide formal privacy guarantees, however, it is generally necessary to put in place additional masking mechanisms. When FL is implemented in wireless systems via uncoded transmission, the channel noise can directly act as a privacy-inducing mechanism. This paper demonstrates that, as long as the privacy constraint level, measured via differential privacy (DP), is below a threshold that decreases with the signal-to-noise ratio (SNR), uncoded transmission achieves privacy “for free”, i.e., without affecting the learning performance. More generally, this work studies adaptive power allocation (PA) for distributed gradient descent in wireless FL with the aim of minimizing the learning optimality gap under privacy and power constraints. Both orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) transmission with “over-the-air-computing” are studied, and solutions are obtained in closed form for an offline optimization setting. Furthermore, heuristic online methods are proposed that leverage iterative one-step-ahead optimization. The importance of dynamic PA and the potential benefits of NOMA versus OMA are demonstrated through extensive simulations.

中文翻译：

---

免费隐私：通过具有自适应功率控制的未编码传输进行无线联合学习

联合学习 (FL) 是指分布式协议，在为共同学习任务进行训练时，避免参与设备之间直接交换原始数据。通过这种方式，FL 可以潜在地减少通过通信泄露的本地数据集的信息。然而，为了提供正式的隐私保证，通常需要设置额外的屏蔽机制。当 FL 通过未编码传输在无线系统中实现时，信道噪声可以直接充当隐私诱导机制。本文证明，只要通过差分隐私 (DP) 测量的隐私约束级别低于随信噪比 (SNR) 降低的阈值，未编码传输就可以“免费”实现隐私，即，在不影响学习成绩的情况下。更普遍，这项工作研究了无线 FL 中分布式梯度下降的自适应功率分配 (PA)，目的是在隐私和功率约束下最小化学习最优差距。研究了具有“空中计算”的正交多址（OMA）和非正交多址（NOMA）传输，并以封闭形式获得了离线优化设置的解决方案。此外，还提出了启发式在线方法，该方法利用迭代的一步超前优化。动态 PA 的重要性以及 NOMA 与 OMA 的潜在优势通过广泛的模拟得到证明。研究了具有“空中计算”的正交多址（OMA）和非正交多址（NOMA）传输，并以封闭形式获得了离线优化设置的解决方案。此外，还提出了启发式在线方法，该方法利用迭代的一步超前优化。动态 PA 的重要性以及 NOMA 与 OMA 的潜在优势通过广泛的模拟得到证明。研究了具有“空中计算”的正交多址（OMA）和非正交多址（NOMA）传输，并以封闭形式获得了离线优化设置的解决方案。此外，还提出了启发式在线方法，该方法利用迭代的一步超前优化。动态 PA 的重要性以及 NOMA 与 OMA 的潜在优势通过广泛的模拟得到证明。