Geodesic
On integer stochastic approximation
Applications of Mathematics, Tome 29 (1984) no. 5, pp. 372-383
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Let $M : \bold R \rightarrow \bold R$ be observable, with experimental errors, at integer points only; unknown elsewhere. Iterative nonparametric procedures for finding the zero point of $M$ are called procedures of integer stochastic approximation. Three types of such procedures (Derman's, Mukerjee's and the authors') are described and compared. A two-dimensional analogue of the third approach is proposed and investigated; its generalization to higher dimensions is conjectured.
Let $M : \bold R \rightarrow \bold R$ be observable, with experimental errors, at integer points only; unknown elsewhere. Iterative nonparametric procedures for finding the zero point of $M$ are called procedures of integer stochastic approximation. Three types of such procedures (Derman's, Mukerjee's and the authors') are described and compared. A two-dimensional analogue of the third approach is proposed and investigated; its generalization to higher dimensions is conjectured.
DOI : 10.21136/AM.1984.104107
Classification : 62L20
Keywords: nonparametric procedures; Robbins-Monro type procedure; integer stochastic approximation 
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Dupač, Václav; Herkenrath, Ulrich. On integer stochastic approximation. Applications of Mathematics, Tome 29 (1984) no. 5, pp. 372-383. doi: 10.21136/AM.1984.104107

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[3] U. Herkenrath: The N-armed bandit with unimodal structure. Metrika 30 (1983), 195 - 210. | DOI | MR | Zbl

[4] A. Kirchen: Überlegungen zur eindimersionalen stochastischen Approximation. Diploma work. University of Bonn, Í982.

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[6] M. B. Neveľson R. Z. Has'minskij: Stochastic Approximation and Recursive Estimation. Translation of Mathem. Monographs, vol. 47, Amer. Mathem. Soc., Providence, 1976. (Russian original, Nauka, Moskva 1982.)

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