Abstract
It is already well known that all stochastic models for learning studied up to now enter the following general scheme (cf.Norman (1972)). The behaviour of the subject on trial n = 0,1,... is determined by his state Sn (an indicator of the subject’s response tendencies) at the beginning of the trial. Sn is a random variable taking on values in a measurable state space (S,S). On trial n an event En +1 occurs that results in a change of state. En +1 is a randon variable taking on values in a measurable event space (E,E) and specifies those occurrences on trial n that affect subsequent behaviour. Typically, En +1. includes a specification of the subject’s response and its observable outcome or payoff. To represent the fact that the occurrence of an event effects a change of state we consider a measurable mapping v of S × E into S and postulate that Sn +1 = v(Sn, En +1), n ≥ 0. Finally, we assume that the conditional probability distribution of En +1 given En, Sn,... depends only on the state Sn and denote it Q(Sn,.).
Dedicated to Professor Octav Onicescu on the occasion of his 9oth birthday
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© 1983 Springer-Verlag New York Inc.
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Iosifescu, M. (1983). Asymptotic Properties of Learning Models. In: Herkenrath, U., Kalin, D., Vogel, W. (eds) Mathematical Learning Models — Theory and Algorithms. Lecture Notes in Statistics, vol 20. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5612-0_9
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DOI: https://doi.org/10.1007/978-1-4612-5612-0_9
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