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

Aplikace matematiky (1980)

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

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topBrůha, 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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- В. И. Варшавский И. П. Воронцова, О поведении стохастических автоматов с переменной структурой, Автоматика и телемеханика 24 (1963), 353 - 360. (1963) Zbl1214.14039MR0163810
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- 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
- I. Brůha, Comparing the theory of deterministic and probabilistic automata for modelling adaptive learning systems, (Czech). Ph. D. thesis, FEL ČVUT, 1973. (1973)
- P. Benedikt, Modelling learning systems by means of probabilistic automata, (Czech). Master Thesis, FEL ČVUT, 1974. (1974)
- K. S. Fu, Stochastic automata as models of learning systems, Proc. Symp. Сор. Information Sci., Columbus, Ohio, 1966. (1966)
- 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
- K. S. Narendra M. A. L. Thathachar, Learnig automata - a survey, IEEE Trans. SMC-4 (1974), 323-334. (1974) MR0469583
- Y. Sawaragi N. Baba, Two $\u03f5$-optimal nonlinear reinforcement schemes for stochastic automata, IEEE Trans. SMC-4 (1974), 126-131. (1974) MR0449946
- R. Viswanathan K. S. Narendra, Games of stochastic automata, IEEE Trans. SMC-4 (1974), 131-135. (1974)
- Z. Kotek I. Brůha V. Chalupa J. Jelínek, Adaptive and learning systems, (Czech). SNTL Praha, 1980. (1980)

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