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Rates of Convergence

  • Harold J. Kushner
  • Dean S. Clark
Part of the Applied Mathematical Sciences book series (AMS, volume 26)

Abstract

In Section 7.1, rate of convergence is defined, and our approach to the rate problem discussed. The rates are developed (in Section 7.3) for three separate cases, two forms of the basic KW procedure and the basic RM procedure. These algorithms are discussed in Section 7.1 and are put into a form which will be useful in the subsequent development. The results of particular interest are the expressions for {Un} given by (7.1.3), (7.1.6) and (7.1.10), and the necessary (resp., best) values for 3 of (7.1.4) ((7.1.5), resp.), and similarly for the other algorithms Section 7.2 gives some notation and lists and discusses several sets of conditions. The rate of convergence theorems are stated and proved in Section 7.3. Section 7.4 contains a discussion of the value of averaging several observations per iteration and compares the basic KW procedure (Theorem 2.3. 5) with the KW procedure when the directions are chosen at random (Theorem 2.3.6).

Keywords

Wiener Process Weak Limit Noise Term Stochastic Approximation Bias Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1978

Authors and Affiliations

  • Harold J. Kushner
    • 1
  • Dean S. Clark
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

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