Differentially Private ADMM Algorithms for Machine Learning

In this paper, we study efficient differentially private alternating direction methods of multipliers (ADMM) via gradient perturbation for many centralized machine learning problems. For smooth convex loss functions with (non)-smooth regularization, propose the first ADMM (DP-ADMM) algorithm performance guarantee (ϵ,δ)-differential privacy ((ϵ,δ)-DP). From viewpoint theoretical analysis, use Gaussian mechanism and conversion relationship between Rényi Differential Privacy (RDP) DP to perform a comprehensive analysis our algorithm. Then establish new criterion prove convergence proposed algorithms including DP-ADMM. We also give utility Moreover, accelerated DP-ADMM (DP-AccADMM) Nesterov’s acceleration technique. Finally, conduct numerical experiments on real-world datasets show privacy-utility tradeoff two algorithms, all comparative shows that DP-AccADMM converges faster has better than DP-ADMM, when budget ϵ is larger threshold.