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Teoriya Veroyatnostei i ee Primeneniya, 1965, Volume 10, Issue 2, Pages 297–300 (Mi tvp523)  

This article is cited in 84 scientific papers (total in 84 papers)

On the stochastic approximation

E. G. Gladyshev

Moscow
Abstract: Using the theory of semimartingal an extention of the well known results oils Robbins–Monro's stochastic approximation method is given. The obtained results. are applied to the least-squares method.
English version:
Theory of Probability and its Applications, 1965, Volume 10, Issue 2, Pages 275–278
DOI: https://doi.org/10.1137/1110031
Bibliographic databases:
Language: Russian
Citation: E. G. Gladyshev, “On the stochastic approximation”, Teor. Veroyatnost. i Primenen., 10:2 (1965), 297–300; Theory Probab. Appl., 10:2 (1965), 275–278
Citation in format AMSBIB
\Bibitem{Gla65}
\by E.~G.~Gladyshev
\paper On the stochastic approximation
\jour Teor. Veroyatnost. i Primenen.
\yr 1965
\vol 10
\issue 2
\pages 297--300
\mathnet{http://mi.mathnet.ru/tvp523}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=185722}
\zmath{https://zbmath.org/?q=an:0147.18002}
\transl
\jour Theory Probab. Appl.
\yr 1965
\vol 10
\issue 2
\pages 275--278
\crossref{https://doi.org/10.1137/1110031}
Linking options:
  • https://www.mathnet.ru/eng/tvp523
  • https://www.mathnet.ru/eng/tvp/v10/i2/p297
  • This publication is cited in the following 84 articles:
    1. M. Vidyasagar, Indian Statistical Institute Series, Probability and Stochastic Processes, 2024, 177  crossref
    2. Rajeeva Laxman Karandikar, Mathukumalli Vidyasagar, “Convergence Rates for Stochastic Approximation: Biased Noise with Unbounded Variance, and Applications”, J Optim Theory Appl, 2024  crossref
    3. Thomas J. Sargent, “Sources of artificial intelligence”, Journal of Economic Dynamics and Control, 2024, 104989  crossref
    4. Aditya Mahajan, Silviu-Iulian Niculescu, Mathukumalli Vidyasagar, 2024 IEEE 63rd Conference on Decision and Control (CDC), 2024, 3877  crossref
    5. M. Vidyasagar, “Convergence of stochastic approximation via martingale and converse Lyapunov methods”, Math. Control Signals Syst., 35:2 (2023), 351  crossref
    6. A. S. Mandel, A. I. Mikhalsky, “On the Work of the Institute of Control Sciences of the Russian Academy of Sciences in the Field of Pattern Recognition Theory and Applications in the 20th Century”, Pattern Recognit. Image Anal., 33:4 (2023), 1593  crossref
    7. Mathukumalli Vidyasagar, “A tutorial introduction to reinforcement learning”, SICE Journal of Control, Measurement, and System Integration, 16:1 (2023), 172  crossref
    8. Barbara Franci, Sergio Grammatico, “Convergence of sequences: A survey”, Annual Reviews in Control, 53 (2022), 161  crossref
    9. M. Vidyasagar, 2022 IEEE 61st Conference on Decision and Control (CDC), 2022, 2319  crossref
    10. Kshama Dwarakanath, Svitlana S Vyetrenko, Tucker Balch, Proceedings of the Second ACM International Conference on AI in Finance, 2021, 1  crossref
    11. Jin Xu, Rongji Mu, Cui Xiong, “A Bayesian stochastic approximation method”, Journal of Statistical Planning and Inference, 211 (2021), 391  crossref
    12. Wenxiao Zhao, “An Introduction to Development of Centralized and Distributed Stochastic Approximation Algorithm with Expanding Truncations”, Algorithms, 14:6 (2021), 174  crossref
    13. Frank E. Curtis, Katya Scheinberg, Rui Shi, “A Stochastic Trust Region Algorithm Based on Careful Step Normalization”, INFORMS Journal on Optimization, 1:3 (2019), 200  crossref
    14. Oleg Rudenko, Oleksandr Bezsonov, Oleh Lebediev, Nataliia Serdiuk, “Robust identification of non-stationary objects with nongaussian interference”, EEJET, 5:4 (101) (2019), 44  crossref
    15. T. P. Krasulina, “On one-sided convergence of a modified stochastic approximation process”, Autom. Remote Control, 79:2 (2018), 286–288  mathnet  crossref  isi  elib
    16. Léon Bottou, Frank E. Curtis, Jorge Nocedal, “Optimization Methods for Large-Scale Machine Learning”, SIAM Rev., 60:2 (2018), 223  crossref
    17. Recursive Identification and Parameter Estimation, 2014, 307  crossref
    18. Michael Kohler, Adam Krzyżak, Harro Walk, “Nonparametric recursive quantile estimation”, Statistics & Probability Letters, 93 (2014), 102  crossref
    19. John Sum, Chi-Sing Leung, Kevin Ho, “Convergence Analyses on On-Line Weight Noise Injection-Based Training Algorithms for MLPs”, IEEE Trans. Neural Netw. Learning Syst., 23:11 (2012), 1827  crossref
    20. J. P. Sum, Chi-Sing Leung, K. I-J Ho, “On-Line Node Fault Injection Training Algorithm for MLP Networks: Objective Function and Convergence Analysis”, IEEE Trans. Neural Netw. Learning Syst., 23:2 (2012), 211  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
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