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Convergence of the Kiefer–Wolfowitz algorithm in the presence of discontinuities

Part of: Stochastic systems and control Mathematical finance

Published online by Cambridge University Press:  23 September 2022

Miklós Rásonyi Open the ORCID record for Miklós Rásonyi [Opens in a new window]  and
Kinga Tikosi
Miklós Rásonyi*
Affiliation:
Rényi Institute, Budapest, and Mathematical Institute, Warsaw
Kinga Tikosi*
Affiliation:
Rényi Institute, Budapest, and Mathematical Institute, Warsaw
*
*Postal address: Reáltanoda utca 13-15, 1053 Budapest, Hungary; ul. Śniadeckich 8, 00-656 Warszawa, Poland.
*Postal address: Reáltanoda utca 13-15, 1053 Budapest, Hungary; ul. Śniadeckich 8, 00-656 Warszawa, Poland.
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Abstract

In this paper we estimate the expected error of a stochastic approximation algorithm where the maximum of a function is found using finite differences of a stochastic representation of that function. An error estimate of the order $n^{-1/5}$ for the nth iteration is achieved using suitable parameters. The novelty with respect to previous studies is that we allow the stochastic representation to be discontinuous and to consist of possibly dependent random variables (satisfying a mixing condition).

Keywords

Stochastic approximationdependent datathreshold strategies

MSC classification

Primary: 93E35: Stochastic learning and adaptive control
Secondary: 91G60: Numerical methods (including Monte Carlo methods)

Information

Type
Original Article
Information
Advances in Applied Probability , Volume 55 , Issue 2 , June 2023 , pp. 382 - 406
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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