Convergence Analysis of Distributed Subgradient Methods over Random Networks

• Main Authors: Lobel, Ilan (Contributor), Ozdaglar, Asuman E. (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor), Massachusetts Institute of Technology. Operations Research Center (Contributor)
• Format: Article
• Language: English
• Published: Institute of Electrical and Electronics Engineers, 2010-11-23T19:13:45Z.
• Subjects: Article
• Online Access: Get fulltext

 We consider the problem of cooperatively minimizing the sum of convex functions, where the functions represent local objective functions of the agents. We assume that each agent has information about his local function, and communicate with the other agents over a time-varying network topology. For this problem, we propose a distributed subgradient method that uses averaging algorithms for locally sharing information among the agents. In contrast to previous works that make worst-case assumptions about the connectivity of the agents (such as bounded communication intervals between nodes), we assume that links fail according to a given stochastic process. Under the assumption that the link failures are independent and identically distributed over time (possibly correlated across links), we provide convergence results and convergence rate estimates for our subgradient algorithm.