Federated Learning with Differential Privacy and Personalized Model Aggregation

Abstract

Federated learning (FL) offers a promising approach to training machine learning models on decentralized data sources without direct data sharing. However, traditional FL methods are vulnerable to information leakage and model divergence, particularly when dealing with highly heterogeneous client datasets. This research proposes a novel framework that combines differential privacy (DP) with personalized model aggregation (PMA) to mitigate these issues. The core claim is that integrating DP safeguards client data while PMA allows for adaptation of the global model to individual client characteristics. We introduce a rigorous methodology for quantifying the trade-offs between privacy, model accuracy, and computational overhead. The proposed approach enhances both the robustness and effectiveness of FL systems, paving the way for more secure and adaptable distributed learning applications. Specifically, we formulate the aggregation process using the following notation: Let $m_i$ represent the model received from client *i*, $s_i$ be the local data used by client *i*, and $\epsilon$ and $\delta$ be the privacy parameters. The personalized aggregation function is defined as: $m_{aggregated} = \frac{\sum_{i=1}^{K} \alpha_i * m_i}{\sum_{i=1}^{K} \alpha_i}$ where $\alpha_i$ are weights determined based on client data characteristics and privacy constraints. We leverage differential privacy by adding noise to the model updates, represented as: $m_i' = m_i + \epsilon * N(0, I_d)$ where $N(0, I_d)$ denotes Gaussian noise with mean 0 and covariance matrix $I_d$ (d-dimensional identity matrix).