Asynchronous Distributed Optimization Over Lossy Networks via Relaxed ADMM: Stability and Linear Convergence

• 成果类型: Article
• 署名作者: Bastianello, Nicola; Carli, Ruggero; Schenato, Luca; Todescato, Marco
• 署名单位: University of Padua
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3011358
• 发表日期: 2021
• 页码: 2620-2635
• 关键词: convergence; Convex functions; Peer-to-peer computing; Computer architecture; cost function; Upper bound; Alternating direction method of multipliers (ADMM); asynchronous update; distributed optimization; lossy communications; operator theory; Peaceman– Rachford splitting (PRS)

摘要

In this article, we focus on the problem of minimizing the sum of convex cost functions in a distributed fashion over a peer-to-peer network. In particular, we are interested in the case in which communications between nodes are prone to failures, and the agents are not synchronized among themselves. We address the problem proposing a modified version of the relaxed alternating direction method of multipliers, which corresponds to the Peaceman-Rachford splitting method applied to the dual. By exploiting results from operator theory, we are able to prove the almost sure convergence of the proposed algorithm under general assumptions on the distribution of communication loss and node activation events. By further assuming the cost functions to be strongly convex, we prove the linear convergence of the algorithm in mean to a neighborhood of the optimal solution and provide an upper bound to the convergence rate. Finally, we present numerical results testing the proposed method in different scenarios.