September, 1951 A Stochastic Approximation Method

Herbert Robbins, Sutton Monro

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.

Citation

Herbert Robbins. Sutton Monro. "A Stochastic Approximation Method." Ann. Math. Statist. 22 (3) 400 - 407, September, 1951. https://doi.org/10.1214/aoms/1177729586

Information

JOURNAL ARTICLE
8 PAGES

Vol.22 • No. 3 • September, 1951