This paper presents a personalized graph federated learning (PGFL) framework in which distributedly connected servers and their respective edge devices collaboratively learn device or cluster-specific models while maintaining the privacy of every individual device. The proposed approach exploits similarities among different models to provide a more relevant experience for each device, even in situations with diverse data distributions and disproportionate datasets. Furthermore, to ensure a secure and efficient approach to collaborative personalized learning, we study a variant of the PGFL implementation that utilizes differential privacy, specifically zero-concentrated differential privacy, where a noise sequence perturbs model exchanges. Our mathematical analysis shows that the proposed privacy-preserving PGFL algorithm converges to the optimal cluster-specific solution for each cluster in linear time. It also shows that exploiting similarities among clusters leads to an alternative output whose distance to the original solution is bounded, and that this bound can be adjusted by modifying the algorithm's hyperparameters. Further, our analysis shows that the algorithm ensures local differential privacy for all clients in terms of zero-concentrated differential privacy. Finally, the performance of the proposed PGFL algorithm is examined by performing numerical experiments in the context of regression and classification using synthetic data and the MNIST dataset.

翻译：本文提出了一种个性化图联邦学习（PGFL）框架，该框架中分布式连接的服务器及其各自的边缘设备在保持每个单独设备隐私的同时，协同学习设备或聚类专属模型。该方法利用不同模型之间的相似性，即使在数据分布多样且数据集规模不均的情况下，也能为每个设备提供更具相关性的体验。此外，为确保协同个性化学习既安全又高效，我们研究了采用差分隐私（具体为零集中差分隐私）的PGFL变体实现方案，其中噪声序列会扰动模型交换。我们的数学分析表明，所提出的隐私保护型PGFL算法能以线性时间收敛到每个聚类的最优聚类专属解。分析同时显示，利用聚类间的相似性会产生一个替代输出，该输出到原始解的距离有界，且此界可通过调整算法超参数进行控制。进一步分析表明，该算法以零集中差分隐私为所有客户端实现局部差分隐私。最后，我们使用合成数据和MNIST数据集，通过回归与分类数值实验对PGFL算法的性能进行了评估。