Federated learning (FL) is a distributed machine learning approach that allows multiple clients to collaboratively train a model without sharing their raw data. To prevent sensitive information from being inferred through the model updates shared in FL, differentially private federated learning (DPFL) has been proposed. DPFL ensures formal and rigorous privacy protection in FL by clipping and adding random noise to the shared model updates. However, the existing DPFL methods often result in severe model utility degradation, especially in settings with data heterogeneity. To enhance model utility, we propose a novel DPFL method named DP$^2$-FedSAM: Differentially Private and Personalized Federated Learning with Sharpness-Aware Minimization. DP$^2$-FedSAM leverages personalized partial model-sharing and sharpness-aware minimization optimizer to mitigate the adverse impact of noise addition and clipping, thereby significantly improving model utility without sacrificing privacy. From a theoretical perspective, we provide a rigorous theoretical analysis of the privacy and convergence guarantees of our proposed method. To evaluate the effectiveness of DP$^2$-FedSAM, we conduct extensive evaluations based on common benchmark datasets. Our results verify that our method improves the privacy-utility trade-off compared to the existing DPFL methods, particularly in heterogeneous data settings.

本研究解决了现有差分隐私联邦学习（DPFL）方法在数据异构环境下模型效用严重下降的问题。我们提出了一种新颖的DPFL方法DP$^2$-FedSAM，结合个性化部分模型共享和敏感度感知最小化优化器，有效提高了模型效用，同时保持隐私保护。实验结果表明，该方法在隐私与效用平衡方面优于现有方法，尤其在异构数据设置中表现突出。

DP$^2$-FedSAM：通过个性化敏感度感知最小化增强差分隐私联邦学习