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Optimal strategies in measurable learning systems on metric spaces

Published online by Cambridge University Press:  14 July 2016

Ernst–Erich Doberkat
Ernst–Erich Doberkat*
Affiliation:
Pädagogische Hochschule Rheinland, Bonn
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Abstract

A dynamic programming approach for the investigation of learning systems is taken. Making use of one-stage decision models and dynamic programs, respectively, two learning models are formulated and the existence of optimal strategies for learning in the respective models is proven.

Keywords

STOCHASTIC MODELS FOR LEARNINGAPPLICATIONS OF ONE-STAGE DECISION MODELSAPPLICATIONS OF DYNAMIC PROGRAMSSET-VALUED MAPPINGS
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 4 , December 1977 , pp. 795 - 805
Copyright
Copyright © Applied Probability Trust 1977 

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References

Berge, C. (1966) Espaces Topologiques—Fonctions Multivoques. Dunod, Paris.Google Scholar
Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Debreu, G. (1967) Integration of correspondences. Proc. 5th Berkeley Symp. Math. Statist. Prob. 2(1), 351–372.Google Scholar
Dubins, L. and Freedman, D. (1964) Measurable sets of measures. Pacific J. Math. 14, 1211–1222.Google Scholar
Himmelberg, C. (1975) Measurable relations. Fund. Math. 87, 53–72.Google Scholar
Hinderer, K. (1970) Foundations of Non-stationary Dynamic Programming with Discrete Time Parameter. Lecture Notes in Operations Research and Mathematical Systems 33, Springer, Berlin.Google Scholar
Klix, F. (1972) Information und Verhalten. Hans Huber, Bern.Google Scholar
Kuratowski, K. (1968) Topology, vol. II. Academic Press, New York.Google Scholar
Menzel, W. (1970) Theorie der Lernsysteme. Springer, Berlin.Google Scholar
Menzel, W. (1973) An extension of the theory of learning-systems. Acta Informatica 2, 357–381.Google Scholar
Michael, E. (1951) Topologies on spaces of subsets. Trans. Amer. Math. Soc. 71, 152–182.Google Scholar
Parthasarathy, K. R. (1967) Probability Measures on Metric Spaces. Academic Press, New York.Google Scholar
Rieder, U. (1975) Bayesian dynamic programming. Adv. Appl. Prob. 7, 330–348.Google Scholar
Schäl, M. (1974) A selection theorem for optimization problems. Arch. Math. 25, 219–224.Google Scholar
Schäl, M. (1975a) Conditions for optimality in dynamic programming and for the limit of n-stage optimal policies to be optimal. Z. Wahrscheinlichkeitsth. 32, 179–196.Google Scholar
Schäl, M. (1975b) On dynamic programming: compactness of the space of policies. Stoch. Proc. Appl. 3, 345–364.Google Scholar