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Exponential Concentration in Stochastic Approximation.

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Τίτλος: Exponential Concentration in Stochastic Approximation.
Συγγραφείς: Law, Kody J. H.1 (AUTHOR) kody.law@manchester.ac.uk, Walton, Neil2 (AUTHOR) neil.walton@durham.ac.uk, Yang, Shangda1 (AUTHOR) shangda.yang@manchester.ac.uk
Πηγή: Operations Research. Jan/Feb2026, Vol. 74 Issue 1, p446-463. 18p.
Θεματικοί όροι: *Markov processes, Stochastic approximation, Ergodic theory, Asymptotic analysis
Περίληψη: We analyze the behavior of stochastic approximation algorithms where iterates, in expectation, progress toward an objective at each step. When progress is proportional to the step size of the algorithm, we prove exponential concentration bounds. These tail-bounds contrast asymptotic normality results, which are more frequently associated with stochastic approximation. The methods that we develop rely on a proof of geometric ergodicity. The extends results on the exponential ergodicity of Markov chains to stochastic approximation algorithms. We apply our results to several different stochastic approximation algorithms, specifically Projected Stochastic Gradient Descent, Kiefer-Wolfowitz, and Stochastic Frank-Wolfe algorithms. When applicable, our results prove faster O(1/t) and linear convergence rates for Projected Stochastic Gradient Descent with a nonvanishing gradient. [ABSTRACT FROM AUTHOR]
Copyright of Operations Research is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Exponential Concentration in Stochastic Approximation.
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  Data: <searchLink fieldCode="JN" term="%22Operations+Research%22">Operations Research</searchLink>. Jan/Feb2026, Vol. 74 Issue 1, p446-463. 18p.
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  Data: We analyze the behavior of stochastic approximation algorithms where iterates, in expectation, progress toward an objective at each step. When progress is proportional to the step size of the algorithm, we prove exponential concentration bounds. These tail-bounds contrast asymptotic normality results, which are more frequently associated with stochastic approximation. The methods that we develop rely on a proof of geometric ergodicity. The extends results on the exponential ergodicity of Markov chains to stochastic approximation algorithms. We apply our results to several different stochastic approximation algorithms, specifically Projected Stochastic Gradient Descent, Kiefer-Wolfowitz, and Stochastic Frank-Wolfe algorithms. When applicable, our results prove faster O(1/t) and linear convergence rates for Projected Stochastic Gradient Descent with a nonvanishing gradient. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Operations Research is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1287/opre.2023.0425
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 18
        StartPage: 446
    Subjects:
      – SubjectFull: Markov processes
        Type: general
      – SubjectFull: Stochastic approximation
        Type: general
      – SubjectFull: Ergodic theory
        Type: general
      – SubjectFull: Asymptotic analysis
        Type: general
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      – TitleFull: Exponential Concentration in Stochastic Approximation.
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            NameFull: Law, Kody J. H.
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            NameFull: Walton, Neil
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              Text: Jan/Feb2026
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              Y: 2026
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