A Stochastic Approximation Method
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.
Permanent link to this document: http://projecteuclid.org/euclid.aoms/1177729586
Digital Object Identifier: doi:10.1214/aoms/1177729586
Mathematical Reviews number (MathSciNet): MR42668
Zentralblatt MATH identifier: 0054.05901