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Distributed dual averaging for convex optimization under communication delays

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2 Author(s)
Konstantinos I. Tsianos ; Department of Electrical and Computer Engineering, McGill University, Montreal, Quebec H3A 2A7, Canada ; Michael G. Rabbat

In this paper we extend and analyze the distributed dual averaging algorithm [1] 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 [1] 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.

Published in:

2012 American Control Conference (ACC)

Date of Conference:

27-29 June 2012