Article
MSC:
62L20,
68D25,
68Q45,
68T05,
68W99,
92A90,
93E03 | MR 0590486 | Zbl 0495.68080 | DOI: 10.21136/AM.1980.103867
Full entry |
PDF
(1.2 MB)
Feedback
PDF
(1.2 MB)
Feedback
Keywords:
learning systems; stochastic automata; convergence of the learning algorithm
learning systems; stochastic automata; convergence of the learning algorithm
Summary:
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.
References:
[1] A. Paz: Introduction to probabilistic automata. Academic Press, New York and London 1971. MR 0289222 | Zbl 0234.94055
[2] M. Л. Цетлин: О поведении конечных автоматов в случайных средах. Автоматика и телемеханика 22 (1961), 1345 - 1354. MR 0141569 | Zbl 1160.68305
[3] В. И. Варшавский И. П. Воронцова: О поведении стохастических автоматов с переменной структурой. Автоматика и телемеханика 24 (1963), 353 - 360. MR 0163810 | Zbl 1214.14039
[4] K. S. Fu T. J. Li: Formulation of learning automata and automata games. Information Sciences 1 (1969), 237-256. DOI 10.1016/S0020-0255(69)80010-1 | MR 0243950
[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. MR 0084911 | Zbl 0072.34701
[6] I. Brůha: Comparing the theory of deterministic and probabilistic automata for modelling adaptive learning systems. (Czech). Ph. D. thesis, FEL ČVUT, 1973.
[7] P. Benedikt: Modelling learning systems by means of probabilistic automata. (Czech). Master Thesis, FEL ČVUT, 1974.
[8] K. S. Fu: Stochastic automata as models of learning systems. Proc. Symp. Сор. Information Sci., Columbus, Ohio, 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. MR 0211798
[10] K. S. Narendra M. A. L. Thathachar: Learnig automata - a survey. IEEE Trans. SMC-4 (1974), 323-334. MR 0469583
[11] Y. Sawaragi N. Baba: Two $\epsilon$-optimal nonlinear reinforcement schemes for stochastic automata. IEEE Trans. SMC-4 (1974), 126-131. MR 0449946
[12] R. Viswanathan K. S. Narendra: Games of stochastic automata. IEEE Trans. SMC-4 (1974), 131-135.
[13] Z. Kotek I. Brůha V. Chalupa J. Jelínek: Adaptive and learning systems. (Czech). SNTL Praha, 1980.
Search
Partner of
