Stochastic approximation: Difference between revisions

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for robust estimation
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==Subsequent developments==
An extensive theoretical literature has grown up around these algorithms, concerning conditions for convergence, rates of convergence, multivariate and other generalizations, proper choice of step size, possible noise models, and so on.<ref name="kushneryin">''Stochastic Approximation Algorithms and Applications'', Harold J. Kushner and G. George Yin, New York: Springer-Verlag, 1997. ISBN 038794916X; 2nd ed., titled ''Stochastic Approximation and Recursive Algorithms and Applications'', 2003, ISBN 0387008942.</ref><ref>''Stochastic Approximation and Recursive Estimation'', Mikhail Borisovich Nevel'son and Rafail Zalmanovich Has'minskiĭ, translated by Israel Program for Scientific Translations and B. Silver, Providence, RI: American Mathematical Society, 1973, 1976. ISBN 0821815970.</ref> These methods are also applied in [[control theory]], in which case the unknown function which we wish to optimize or find the zero of may vary in time. In this case, the step size <math>a_n</math> should not converge to zero but should be chosen so as to track the function.<ref name="kushneryin"/><sup>, 2nd ed., chapter 3</sup>
 
[[C. Johan Masreliez]] and [[R. Douglas Martin]] were the first to use
stochastc approximation in 1975 when dealing with [[Robust statistics|robust]] [[estimation]].<ref>R.D. Martin & C.J. Masreliez, ''Robust estimation via stochastic approximation''. IEEE Trans. Inform. Theory, 21(pp.263—271) (1975).</ref>
 
==See also==
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*[[Stochastic optimization]]
*[[Simultaneous perturbation stochastic approximation]]
 
 
==References==