A Stochastic Approximation Method
Robbins, Herbert ; Monro, Sutton
Ann. Math. Statist., Tome 22 (1951) no. 4, p. 400-407 / Harvested from Project Euclid
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Let $M(x)$ denote the expected value at level $x$ of the response to a certain experiment. $M(x)$ is assumed to be a monotone function of $x$ but is unknown to the experimenter, and it is desired to find the solution $x = \theta$ of the equation $M(x) = \alpha$, where $\alpha$ is a given constant. We give a method for making successive experiments at levels $x_1,x_2,\cdots$ in such a way that $x_n$ will tend to $\theta$ in probability.
Publié le : 1951-09-14
Classification:  
@article{1177729586,
     author = {Robbins, Herbert and Monro, Sutton},
     title = {A Stochastic Approximation Method},
     journal = {Ann. Math. Statist.},
     volume = {22},
     number = {4},
     year = {1951},
     pages = { 400-407},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177729586}
}

Robbins, Herbert; Monro, Sutton. A Stochastic Approximation Method. Ann. Math. Statist., Tome 22 (1951) no. 4, pp.  400-407. http://gdmltest.u-ga.fr/item/1177729586/