QADMM+DP: A Privacy-Preserving Paradigm for Communication-Efficient Federated Learning

Federated learning (FL) faces two critical barriers in real-world deployment: privacy vulnerabilities and high communication overhead. This paper introduces QADMM+DP, a novel federated learning framework that integrates stochastic quantization with differential privacy into the ADMM backbone, delivering rigorous privacy guarantees and minimum communication cost. We provide a unified convergence analysis covering both convex and nonconvex problems under simultaneous quantization and Gaussian noise. For convex (possibly nondifferentiable) functions, we prove convergence to a neighborhood of the optimal solution, with the radius explicitly bounded by the privacy and quantization noise. For smooth nonconvex losses, we establish convergence to a stationary neighborhood, quantifying the trade-off between noise injection and stationarity error. Crucially, our quantization strategy compresses model updates without biasing the learning trajectory, while differential privacy ensures resilience against gradient and model inversion attacks. This work presents a unified convergence analysis for federated ADMM under simultaneous quantization and DP perturbations, covering both convex and nonconvex objectives, with explicit noise-dominated neighborhood bounds that precisely quantify the privacy-accuracy trade-off. Experimental results on linear regression (convex problem) and image classification using deep learning (nonconvex problem) tasks show that QADMM+DP nearly matches the convergence speed of full-precision ADMM, yet reduces communication payloads by an order of magnitude and preserves privacy. This work bridges the gap between privacy, efficiency, and convergence in distributed learning, offering a scalable and secure paradigm for next-generation FL systems.