When Differential Privacy Meets Wireless Federated Learning: An Improved Analysis for Privacy and Convergence

Federated Learning (FL) is a distributed learning paradigm that preserves privacy by eliminating the need to exchange raw data during training. In its prototypical edge instantiation with underlying wireless transmissions enabled by analog over-the-air computing (AirComp), referred to as over-the-air FL (AirFL), the inherent channel noise plays a unique role of frenemy in the sense that it degrades training due to noisy global aggregation while providing a natural source of randomness for privacy-preserving mechanisms, formally quantified by differential privacy (DP). It remains, nevertheless, challenging to effectively harness such channel impairments, as prior arts, under assumptions of either simple channel models or restricted types of loss functions, mostly considering (local) DP enhancement with a single-round or non-convergent bound on privacy loss. In this paper, we study AirFL over multiple-access fading channels with a multi-antenna base station (BS) subject to user-level DP requirements. Despite a recent study, which claimed in similar settings that artificial noise (AN) must be injected to ensure DP in general, we demonstrate, on the contrary, that DP can be gained as a perk even without employing any AN. Specifically, we derive a novel bound on DP that converges under general bounded-domain assumptions on model parameters, along with a convergence bound with general smooth and non-convex loss functions. Next, we optimize over receive beamforming and power allocations to characterize the optimal convergence-privacy trade-offs, which also reveal explicit conditions in which DP is achievable without compromising training. Finally, our theoretical findings are validated by extensive numerical results.

Balancing convergence efficiency and robustness under Differential Privacy (DP) is a central challenge in Federated Learning (FL). While AdamW accelerates training and fine-tuning in large-scale models, we find that directly applying it to Differentially Private FL (DPFL) suffers from three major issues: (i) data heterogeneity and privacy noise jointly amplify the variance of second-moment estimator, (ii) DP perturbations bias the second-moment estimator, and (iii) DP amplify AdamW sensitivity to local overfitting, worsening client drift. We propose DP-FedAdamW, the first AdamW-based optimizer for DPFL. It restores AdamW under DP by stabilizing second-moment variance, removing DP-induced bias, and aligning local updates to the global descent to curb client drift. Theoretically, we establish an unbiased second-moment estimator and prove a linearly accelerated convergence rate without any heterogeneity assumption, while providing tighter $(\varepsilon,δ)$-DP guarantees. Our empirical results demonstrate the effectiveness of DP-FedAdamW across language and vision Transformers and ResNet-18. On Tiny-ImageNet (Swin-Base, $\varepsilon=1$), DP-FedAdamW outperforms the state-of-the-art (SOTA) by 5.83%. The code is available in Appendix.

Differentially private federated learning must balance privacy protection against model accuracy and training efficiency. Static gradient clipping applies a fixed threshold throughout training and across model layers, which can cause excessive clipping when the threshold is too small or unnecessarily large noise when it is too large. This paper presents DDP-SA-adaptive, an adaptive gradient clipping and noise adding mechanism for differentially private federated learning with secure aggregation. At each communication round, every client determines a separate clipping threshold for each model layer from the median of its per-sample gradient norms. The resulting layer-wise thresholds adapt to the evolving gradient distributions and calibrate the Laplace noise added before the updates are encoded and secret-shared among intermediate aggregation servers. We evaluate the proposed mechanism on a federated regression task in terms of efficiency, accuracy, privacy, convergence, clipping norm, and noise magnitude. Compared with the static DDP-SA baseline, DDP-SA-adaptive reduces the number of communication rounds by 6.81%, total training time by 19.21%, and average per-round training time by 13.33%, leading to improved training efficiency. It also reduces test loss by 98.74% and increases test R2 by 3.41%, leading to improved model accuracy. To attain R2 = 0.99, the adaptive mechanism operates with a privacy budget of approximately epsilon = 0.1, compared with epsilon = 0.4 for static DDP-SA, thus providing stronger privacy protection and achieving stronger privacy guarantees. These results demonstrate that round-wise, layer-wise adaptation can improve the privacy-accuracy-efficiency trade-off of differentially private federated learning.