Asynchronous Broadcast-Based Convex Optimization Over a Network

• Published in: IEEE transactions on automatic control Vol. 56; no. 6; pp. 1337 - 1351
• Main Author: Nedic, A
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2011; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Artificial intelligence; Asynchronous algorithms; Clocks; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Convergence; convex optimization; distributed multi-agent system; Exact sciences and technology; Markov processes; Optimization; random broadcast network; Sensors; Software; Symmetric matrices; Almost sure convergence; Probabilistic approach; distributed multi-agent system; Bounded error; Interconnected power system; Error bound; Network management; Distributed system; Communication network; Set constraint; Convex programming; random broadcast network; Value function; Multiagent system; Asynchronous algorithms; Broadcasting; Wireless network; convex optimization; Convex function; Objective function; Artificial intelligence; Asynchronous transmission
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2010.2079650

We consider a distributed multi-agent network system where each agent has its own convex objective function, which can be evaluated with stochastic errors. The problem consists of minimizing the sum of the agent functions over a commonly known constraint set, but without a central coordinator and without agents sharing the explicit form of their objectives. We propose an asynchronous broadcast-based algorithm where the communications over the network are subject to random link failures. We investigate the convergence properties of the algorithm for a diminishing (random) stepsize and a constant stepsize, where each agent chooses its own stepsize independently of the other agents. Under some standard conditions on the gradient errors, we establish almost sure convergence of the method to an optimal point for diminishing stepsize. For constant stepsize, we establish some error bounds on the expected distance from the optimal point and the expected function value. We also provide numerical results.