## The Annals of Mathematical Statistics

### A Stochastic Approximation Method

#### Abstract

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.

#### Article information

Source
Ann. Math. Statist. Volume 22, Number 3 (1951), 400-407.

Dates
First available: 28 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoms/1177729586

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aoms/1177729586

Mathematical Reviews number (MathSciNet)
MR42668

Zentralblatt MATH identifier
0054.05901

#### Citation

Robbins, Herbert; Monro, Sutton. A Stochastic Approximation Method. The Annals of Mathematical Statistics 22 (1951), no. 3, 400--407. doi:10.1214/aoms/1177729586. http://projecteuclid.org/euclid.aoms/1177729586.