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| GangYIN,LeYiWANG,YuSUN,DavidCASBEER,RaymondHOLSAPPLE,DerekKINGSTON |
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| (Department of Mathematics, Wayne State University;Department of Electrical and Computer Engineering, Wayne State University;Quantitative Business Analysis Department, Siena College;Control Science Center of Excellence, Air Force Research Laboratory) |
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| Received:January 20, 2012Revised:May 23, 2012 |
| 基金项目:The research of G. Yin and L. Y. Wang was partly supported by the U.S. Army Research Office (No. W911NF-12-1-0223). |
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| Asymptotic optimality for consensus-type stochastic approximation algorithms using iterate averaging |
| Gang YIN,Le Yi WANG,Yu SUN,David CASBEER,Raymond HOLSAPPLE,Derek KINGSTON |
| (Department of Mathematics, Wayne State University;Department of Electrical and Computer Engineering, Wayne State University;Quantitative Business Analysis Department, Siena College;Control Science Center of Excellence, Air Force Research Laboratory) |
| Abstract: |
| This paper introduces a post-iteration averaging algorithm to achieve asymptotic optimality in convergence rates of stochastic approximation algorithms for consensus control with structural constraints. The algorithm involves two stages. The first stage is a coarse approximation obtained using a sequence of large stepsizes. Then, the second stage provides a refinement by averaging the iterates from the first stage. We show that the new algorithm is asymptotically efficient and gives the optimal convergence rates in the sense of the best scaling factor and ‘smallest’ possible asymptotic variance. |
| Key words: Stochastic approximation algorithm Consensus Iterate averaging Asymptotic optimality |
