Federated Logistic Regression with Enhanced Privacy: A Dynamic Gaussian Perturbation Approach via ADMM from an...

Federated learning enables distributed model training across edge nodes without direct raw data sharing, but model parameter transmission still poses significant privacy risks. To address this vulnerability, a Distributed Logistic Regression Gaussian Perturbation (DLGP) algorithm is proposed, which integrates the Alternating Direction Method of Multipliers (ADMM) with a calibrated differential privacy mechanism. The centralized logistic regression problem is decomposed into local subproblems that are solved independently on edge nodes, where only perturbed model parameters are shared with a central server. The Gaussian noise injection mechanism is designed to optimize the privacy-utility trade-off by introducing calibrated uncertainty into parameter updates, effectively obscuring sensitive information while preserving essential model characteristics. The ℓ2-sensitivity of local updates is derived, and a rigorous (ϵ,δ)-differential privacy guarantee is provided. Evaluations are conducted on a real-world dataset, and it is demonstrated that DLGP maintains favorable performance across varying privacy budgets, numbers of nodes, and penalty parameters.