ADMM-Tracking Gradient for Distributed Optimization Over Asynchronous and Unreliable Networks

• 成果类型: Article
• 署名作者: Carnevale, Guido; Bastianello, Nicola; Notarstefano, Giuseppe; Carli, Ruggero
• 署名单位: University of Bologna; Royal Institute of Technology; University of Padua
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3539454
• 发表日期: 2025
• 关键词: DYNAMIC AVERAGE CONSENSUS; algorithm; CONVERGENCE; STABILITY

摘要

In this article, we propose a novel distributed algorithm for consensus optimization over networks and a robust extension tailored to deal with asynchronous agents and packet losses. Indeed, to robustly achieve dynamic consensus on the solution estimates and the global descent direction, we embed in our algorithms a distributed implementation of the alternating direction method of multipliers. Such a mechanism is suitably interlaced with a local proportional action steering each agent estimate to the solution of the original consensus optimization problem. First, in the case of ideal networks, by using tools from system theory, we prove the linear convergence of the scheme with strongly convex costs. Then, by exploiting the averaging theory, we extend such a first result to prove that the robust extension of our method preserves linear convergence in the case of asynchronous agents and packet losses. Further, by using the notion of input-to-state stability, we also guarantee the robustness of the schemes with respect to additional, generic errors affecting the agents' updates. Finally, some numerical simulations confirm our theoretical findings and compare our algorithms with other distributed schemes in terms of speed and robustness.