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.
Keywords
MathematicsMonotone polygonConstant (computer programming)Alpha (finance)Function (biology)Expected valueValue (mathematics)CombinatoricsApplied mathematicsStatisticsGeometryComputer science
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Publication Info
- Year
- 1951
- Type
- article
- Volume
- 22
- Issue
- 3
- Pages
- 400-407
- Citations
- 9197
- Access
- Closed
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Cite This
Herbert Robbins,
Sutton Monro
(1951).
A Stochastic Approximation Method.
The Annals of Mathematical Statistics
, 22
(3)
, 400-407.
https://doi.org/10.1214/aoms/1177729586
Identifiers
- DOI
- 10.1214/aoms/1177729586