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In this paper we extend and analyze the distributed dual averaging algorithm  to handle communication delays and general stochastic consensus protocols. Assuming each network link experiences some fixed bounded delay, we show that distributed dual averaging converges and the error decays at a rate O(T-0.5) where T is the number of iterations. This bound is an improvement over  by a logarithmic factor in T for networks of fixed size. Finally, we extend the algorithm to the case of using general non-averaging consensus protocols. We prove that the bias introduced in the optimization can be removed by a simple correction that depends on the stationary distribution of the consensus matrix.
American Control Conference (ACC), 2012
Date of Conference: 27-29 June 2012