Learning extremal regulator implementation by a stochastic automaton and stochastic approximation theory

Ivan Brůha

Aplikace matematiky (1980)

  • Volume: 25, Issue: 5, page 315-323
  • ISSN: 0862-7940

Abstract

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There exist many different approaches to the investigation of the characteristics of learning system. These approaches use different branches of mathematics and, thus, obtain different results, some of them are too complicated and others do not match the results of practical experiments. This paper presents the modelling of learning systems by means of stochastic automate, mainly one particular model of a learning extremal regulator. The proof of convergence is based on Dvoretzky's Theorem on stochastic approximations. Experiments have proved the theory of stochastic automata and stochastic approximations to be quite suitable means for studying the learning systems.

How to cite

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Brůha, Ivan. "Learning extremal regulator implementation by a stochastic automaton and stochastic approximation theory." Aplikace matematiky 25.5 (1980): 315-323. <http://eudml.org/doc/15156>.

@article{Brůha1980,
abstract = {There exist many different approaches to the investigation of the characteristics of learning system. These approaches use different branches of mathematics and, thus, obtain different results, some of them are too complicated and others do not match the results of practical experiments. This paper presents the modelling of learning systems by means of stochastic automate, mainly one particular model of a learning extremal regulator. The proof of convergence is based on Dvoretzky's Theorem on stochastic approximations. Experiments have proved the theory of stochastic automata and stochastic approximations to be quite suitable means for studying the learning systems.},
author = {Brůha, Ivan},
journal = {Aplikace matematiky},
keywords = {learning systems; stochastic automata; convergence of the learning algorithm; learning systems; stochastic automata; convergence of the learning algorithm},
language = {eng},
number = {5},
pages = {315-323},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Learning extremal regulator implementation by a stochastic automaton and stochastic approximation theory},
url = {http://eudml.org/doc/15156},
volume = {25},
year = {1980},
}

TY - JOUR
AU - Brůha, Ivan
TI - Learning extremal regulator implementation by a stochastic automaton and stochastic approximation theory
JO - Aplikace matematiky
PY - 1980
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 25
IS - 5
SP - 315
EP - 323
AB - There exist many different approaches to the investigation of the characteristics of learning system. These approaches use different branches of mathematics and, thus, obtain different results, some of them are too complicated and others do not match the results of practical experiments. This paper presents the modelling of learning systems by means of stochastic automate, mainly one particular model of a learning extremal regulator. The proof of convergence is based on Dvoretzky's Theorem on stochastic approximations. Experiments have proved the theory of stochastic automata and stochastic approximations to be quite suitable means for studying the learning systems.
LA - eng
KW - learning systems; stochastic automata; convergence of the learning algorithm; learning systems; stochastic automata; convergence of the learning algorithm
UR - http://eudml.org/doc/15156
ER -

References

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  1. A. Paz, Introduction to probabilistic automata, Academic Press, New York and London 1971. (1971) Zbl0234.94055MR0289222
  2. M. Л. Цетлин, О поведении конечных автоматов в случайных средах, Автоматика и телемеханика 22 (1961), 1345 - 1354. (1961) Zbl1160.68305MR0141569
  3. В. И. Варшавский И. П. Воронцова, О поведении стохастических автоматов с переменной структурой, Автоматика и телемеханика 24 (1963), 353 - 360. (1963) Zbl1214.14039MR0163810
  4. K. S. Fu T. J. Li, 10.1016/S0020-0255(69)80010-1, Information Sciences 1 (1969), 237-256. (1969) MR0243950DOI10.1016/S0020-0255(69)80010-1
  5. A. Dvoretzky, On stochastic approximation, Proc. 3rd Berkeley Symp. Math. Statist, and Probability, vol. 1, 39-55, Univ. of California Press, Berkeley, Cal., 1956. (1956) Zbl0072.34701MR0084911
  6. I. Brůha, Comparing the theory of deterministic and probabilistic automata for modelling adaptive learning systems, (Czech). Ph. D. thesis, FEL ČVUT, 1973. (1973) 
  7. P. Benedikt, Modelling learning systems by means of probabilistic automata, (Czech). Master Thesis, FEL ČVUT, 1974. (1974) 
  8. K. S. Fu, Stochastic automata as models of learning systems, Proc. Symp. Сор. Information Sci., Columbus, Ohio, 1966. (1966) 
  9. K. S. Fu Z. J. Nikolic, On some reinforcement techniques and their relation to the stochastic approximation, IEEE Trans. AC-11 (1966), 756-758. (1966) MR0211798
  10. K. S. Narendra M. A. L. Thathachar, Learnig automata - a survey, IEEE Trans. SMC-4 (1974), 323-334. (1974) Zbl0279.68067MR0469583
  11. Y. Sawaragi N. Baba, Two ϵ -optimal nonlinear reinforcement schemes for stochastic automata, IEEE Trans. SMC-4 (1974), 126-131. (1974) Zbl0276.94021MR0449946
  12. R. Viswanathan K. S. Narendra, Games of stochastic automata, IEEE Trans. SMC-4 (1974), 131-135. (1974) Zbl0294.94031
  13. Z. Kotek I. Brůha V. Chalupa J. Jelínek, Adaptive and learning systems, (Czech). SNTL Praha, 1980. (1980) 

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