ML Anthology

A Stochastic Approximation Method

Herbert Robbins, Sutton Monro
Notable Works 1951 pp. 400-407
doi:10.1214/aoms/1177729586 /misc/1951/robbins1951misc-stochastic/

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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Text

Robbins and Monro. "A Stochastic Approximation Method." Annals of Mathematical Statistics, 1951. doi:10.1214/aoms/1177729586

Markdown

[Robbins and Monro. "A Stochastic Approximation Method." Annals of Mathematical Statistics, 1951.](https://mlanthology.org/misc/1951/robbins1951misc-stochastic/) doi:10.1214/aoms/1177729586

BibTeX

@misc{robbins1951misc-stochastic,
  title     = {{A Stochastic Approximation Method}},
  author    = {Robbins, Herbert and Monro, Sutton},
  howpublished = {Annals of Mathematical Statistics},
  year      = {1951},
  pages     = {400-407},
  doi       = {10.1214/aoms/1177729586},
  volume    = {22},
  number    = {3},
  url       = {https://mlanthology.org/misc/1951/robbins1951misc-stochastic/}
}