4.7 Article

ZONE: Zeroth-Order Nonconvex Multiagent Optimization Over Networks

Journal

IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 64, Issue 10, Pages 3995-4010

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2019.2896025

Keywords

Distributed optimization; nonconvex optimization; primal-dual algorithms; zeroth-order information

Funding

  1. National Science Foundation [CMMI-1727757, CCF-1526078]
  2. Air Force Office of Scientific Research [15RT0767]

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In this paper, we consider distributed optimization problems over a multiagent network, where each agent can only partially evaluate the objective function, and it is allowed to exchange messages with its immediate neighbors. Differently from all existing works on distributed optimization, our focus is given to optimizing a class of nonconvex problems and under the challenging setting, where each agent can only access the zeroth-order information (i.e., the functional values) of its local functions. For different types of network topologies, such as undirected connected networks or star networks, we develop efficient distributed algorithms and rigorously analyze their convergence and rate of convergence (to the set of stationary solutions). Numerical results are provided to demonstrate the efficiency of the proposed algorithms.

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