Asymptotic optimality for consensus-type stochastic approximation algorithms using iterate averaging

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 seq...

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Bibliographic Details
Published in:Journal of control theory and applications 2013-02, Vol.11 (1), p.1-9
Main Authors: Yin, Gang, Wang, Le Yi, Sun, Yu, Casbeer, David, Holsapple, Raymond, Kingston, Derek
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Asymptotic properties
Complexity
Computational Intelligence
Control
Control and Systems Theory
Control theory
Convergence
Engineering
Mathematical analysis
Mechatronics
Optimization
Robotics
Stochasticity
Systems Theory
平均
最优收敛速度
渐近方差
渐近最优
渐近有效
近似算法
迭代点
随机逼近算法
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Summary: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.
ISSN:1672-6340
1993-0623
DOI:10.1007/s11768-013-2013-2