### A Stochastic Approximation Method

Herbert Robbins and Sutton Monro
Source: Ann. Math. Statist. Volume 22, Number 3 (1951), 400-407.

#### 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.

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