Randomized Gradient-Free Method for Multiagent Optimization Over Time-Varying Networks

• Published in: IEEE transaction on neural networks and learning systems Vol. 26; no. 6; pp. 1342 - 1347
• Main Authors: Deming Yuan, Ho, Daniel W. C.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.06.2015
• Subjects: Average consensus; Convergence; distributed multiagent system; distributed optimization; Learning systems; Linear programming; Network topology; networked control systems; Optimization; Smoothing methods; Vectors; distributed multiagent system; networked control systems; distributed optimization; Average consensus
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2014.2336806

In this brief, we consider the multiagent optimization over a network where multiple agents try to minimize a sum of nonsmooth but Lipschitz continuous functions, subject to a convex state constraint set. The underlying network topology is modeled as time varying. We propose a randomized derivative-free method, where in each update, the random gradient-free oracles are utilized instead of the subgradients (SGs). In contrast to the existing work, we do not require that agents are able to compute the SGs of their objective functions. We establish the convergence of the method to an approximate solution of the multiagent optimization problem within the error level depending on the smoothing parameter and the Lipschitz constant of each agent's objective function. Finally, a numerical example is provided to demonstrate the effectiveness of the method.