Resource-Aware Exact Decentralized Optimization Using Event-Triggered Broadcasting

• 成果类型: Article
• 署名作者: Liu, Changxin; Li, Huiping; Shi, Yang
• 署名单位: University of Victoria; Northwestern Polytechnical University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3014316
• 发表日期: 2021
• 页码: 2961-2974
• 关键词: Augmented Lagrangian method; decentralized optimization; event-triggered broadcasting; inexact method

摘要

This article addresses the decentralized optimization problem where a group of agents with coupled private objective functions work together to exactly optimize the summation of local interests. Upon modeling the decentralized problem as an equality-constrained centralized one, we leverage the linearized augmented Lagrangian method to design an event-triggered decentralized algorithm that only requires light local computation at generic time instants and peer-to-peer communication at sporadic triggering time instants. The triggering time instants for each agent are locally determined by comparing the deviation between true and broadcast primal variables with certain triggering thresholds. Provided that the threshold is summable over time, we establish a new upper bound for the effect of triggering behavior on the primal-dual residual. Based on this, the same convergence rate O(1/k) with periodic algorithms is secured for nonsmooth convex problems. Stronger convergence results are obtained for strongly convex and smooth problems, that is, the iterates linearly converge with exponentially decaying triggering thresholds. Finally, the developed strategy is examined with two common optimization problems; comparison results illustrate its performance and superiority in exploiting communication resources.