Federated Logistic Regression with Enhanced Privacy: A Dynamic Gaussian Perturbation Approach via ADMM from an Information-Theoretic Perspective

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.