Privacy-Preserving Distributed ADMM With Event-Triggered Communication

• Published in: IEEE transaction on neural networks and learning systems Vol. 35; no. 2; pp. 2835 - 2847
• Main Authors: Zhang, Zhen, Yang, Shaofu, Xu, Wenying, Di, Kai
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.02.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Alternating direction method of multipliers (ADMM); Approximation algorithms; Communication; Computation; Convergence; Convex functions; Costs; distributed optimization; event-triggered communication; Hessian matrices; Iterative methods; Linear programming; Mathematical analysis; Mathematical models; Objective function; Optimization; Privacy; privacy preserving; Schedules
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2022.3192346

This article addresses distributed optimization problems, in which a group of agents cooperatively minimize the sum of their private objective functions via information exchanging. Building on alternating direction method of multipliers (ADMM), we propose a privacy-preserving and communication-efficient decentralized quadratically approximated ADMM algorithm, termed PC-DQM, for solving such type of problems under the scenario of limited communication. In PC-DQM, an event-triggered mechanism is designed to schedule the communication instants for reducing communication cost. Simultaneously, for privacy preservation, a Hessian matrix with perturbed noise is introduced to quadratically approximate the objective function, which results in a closed form of primal vector update and then avoids solving a subproblem at each iteration with possible high computation cost. In addition, the triggered scheme is also utilized to schedule the update of Hessian, which can also reduce computation cost. We theoretically show that PC-DQM can protect privacy but without losing accuracy. In addition, we rigorously prove that PC-DQM converges linearly to the exact optimal solution for strongly convex and smooth objective functions. Finally, numerical simulation is presented to illustrate the effectiveness and efficiency of our algorithm.