Asynchronous Optimization Over Graphs: Linear Convergence Under Error Bound Conditions

• 成果类型: Article
• 署名作者: Cannelli, Loris; Facchinei, Francisco; Scutari, Gesualdo; Kungurtsev, Vyacheslav
• 署名单位: Universita della Svizzera Italiana; Purdue University System; Purdue University; Sapienza University Rome; Czech Technical University Prague
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3033490
• 发表日期: 2021
• 页码: 4604-4619
• 关键词: Delays; optimization; CONVERGENCE; Partitioning algorithms; nickel; linear programming; indexes; asynchronous algorithms; error bounds; linear rate; multiagent systems; Nonconvex Optimization

摘要

We consider convex and nonconvex constrained optimization with a partially separable objective function: Agents minimize the sum of local objective functions, each of which is known only by the associated agent and depends on the variables of that agent and those of a few others. This partitioned setting arises in several applications of practical interest. We propose what is, to the best of our knowledge, the first distributed, asynchronous algorithm with rate guarantees for this class of problems. When the objective function is nonconvex, the algorithm provably converges to a stationary solution at a sublinear rate whereas linear rate is achieved under the renowned Luo-Tseng error bound condition (which is less stringent than strong convexity). Numerical results on matrix completion and LASSO problems show the effectiveness of our method.