University Of Tehran Press Journal of Algorithms and Computation 2476-2776 57 2 2025 12 31 ADMM-DP: A Distributed and Privacy-Preserving Optimization Framework for Scalable Machine Learning in Information Systems 25 65 106205 10.22059/jac.2025.404651.1245 EN Arvin Asadi Department of Mathematical Sciences Sharif University of Technology, Tehran, Iran Mahsa Saadat Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran 0000-0003-1698-5011 Journal Article 2025 11 01 Recent advances in federated learning and IoT-driven edge analytics underscore the need for optimization techniques that are both scalable and privacy-preserving[1][2]. In this work, we introduce ADMM-DP, a variant of the Alternating Direction Method of Multipliers that seamlessly integrates differential privacy (DP) guarantees in a fully decentralized, multi-agent learning architecture[3]. ADMM-DP leverages an augmented Lagrangian formulation with adaptive inexact local updates and calibrated Gaussian noise injection into each exchanged message, ensuring rigorous (ε,δ)-DP without sacrificing convergence[4][5]. Theoretically, we establish convergence rates and privacy-utility bounds under realistic heterogeneous (non-IID) data conditions. Building on DP-ADMM literature, we prove that ADMM-DP converges to a stationary solution with an explicit utility-privacy tradeoff[6], and furthermore, for strongly convex losses the method attains linear convergence rates comparable to non-private ADMM[7]. Privacy loss is tracked via advanced composition (moments accountant) to yield tight end-to-end DP guarantees[8]. https://jac.ut.ac.ir/article_106205_e879b179f8a2ce9b06c6ee8b39e9256d.pdf