Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling

Details Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling

2010-05-12

arxiv.org/abs/1005.2012v3

IEEE Transactions on Automatic Control 57(3), pp. 592 - 606. March 2012

Mathematics

Optimization and Control

40 pages, 4 figures

Scientific paper

10.1109/TAC.2011.2161027

The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains, including distributed tracking and localization, multi-agent co-ordination, estimation in sensor networks, and large-scale optimization in machine learning. We develop and analyze distributed algorithms based on dual averaging of subgradients, and we provide sharp bounds on their convergence rates as a function of the network size and topology. Our method of analysis allows for a clear separation between the convergence of the optimization algorithm itself and the effects of communication constraints arising from the network structure. In particular, we show that the number of iterations required by our algorithm scales inversely in the spectral gap of the network. The sharpness of this prediction is confirmed both by theoretical lower bounds and simulations for various networks. Our approach includes both the cases of deterministic optimization and communication, as well as problems with stochastic optimization and/or communication.

Affiliated with

Also associated with

No associations

Rating

Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-499008