A CORRELATED URN-SCHEME FOR A CONTINUUM OF RESPONSES.
Abstract
A new model to cover the case of simple learning with a continuum of responses is presented and analysed. Called a correlated urn-scheme, it is an adaption of the continuous analog of the classical urnscheme for learning. The behavior of the model under non-contingent reinforcement is investigated and tests of the applicability of the model are derived. Sufficient conditions, relating to reinforcement schedules, for ergodic behavior in the case of contingent reinforcement are developed using a theorem due to Ionescu-Tulcea. The relation of the correlated urn-scheme to existing models is discussed (with much attention to the much used linear model); and possible generalizations of the urn-scheme are suggested. An empirical comparison with the linear model is presented. The urn-scheme predicts the same asymptotic response distribution as the linear model but differs in its prediction of sequential dependencies. By this is meant that the urn-scheme and the linear model predict different asymptotic response distributions conditioned on preceding responses and/or reinforcements. That the unconditional response distribution is in good correspondence with observation, has been verified in a number of papers; as has the fact that the linear model's predicted conditional distributions are unsatisfactory. The urn-scheme shows a significant improvement in this area of prediction, as indicated by the included empirical comparison. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 20, 1965
- Accession Number
- AD0623171
Entities
People
- Barry Charles Arnold
Organizations
- Stanford University