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A Stochastic Approximation Method

1951/09/01 by Herbert Robbins, Sutton Monro · 9,641 citations
Decision Sciences · Mathematics · #Alpha (finance) #Applied mathematics #Combinatorics #Computer science #Constant (computer programming) #Expected value #Function (biology) #Geometry #Mathematics #Monotone polygon #Optimal Experimental Design Methods #Statistics #Value (mathematics)

paper · pdf · doi:10.1214/aoms/1177729586

published in The Annals of Mathematical Statistics 22(3), 400-407 (Institute of Mathematical Statistics)

openalex publication_date 1951/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 = θ of the equation M(x) = α, where α is a given constant. We give a method for making successive experiments at levels x1,x2,⋯ in such a way that xn will tend to θ in probability.

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