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Analysis of Stochastic Gradient Algorithms for Linear Regression Problems
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
1983 (English)Report (Other academic)
Abstract [en]

Parameter estimation problems that can be formulated as linear regressions are quite common in many applications. Recursive (on-line, sequential) estimation of such parameters can be performed using the recursive least squares (RLS) algorithm or a stochastic gradient version of this algorithm. In this paper the convergence properties of the gradient algorithm are analyzed under the assumption that the gain tends to zero. The technique is the same as the so-called ordinary differential equation approach, but the treatment here is self-contained and includes a proof of the boundedness of the estimates. A main result is that the convergence conditions for the gradient algorithm are the same as those for the recursive least squares algorithm.

Place, publisher, year, edition, pages
Linköping: Linköping University , 1983. , 38 p.
LiTH-ISY-I, ISSN 8765-4321 ; 587
Keyword [en]
Gradient methods, Least-squares estimation, Parameter estimation, Stochastic approximation
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-104392OAI: diva2:696887
Available from: 2014-02-16 Created: 2014-02-16 Last updated: 2014-02-16

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Ljung, Lennart
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Automatic ControlThe Institute of Technology
Control Engineering

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