Contributions of minimax theory to instructional decision making in intelligent tutoring systems

Abstract

The purpose of this paper is to formulate decision rules for adapting the appropriate amount of instruction to learning needs in intelligent tutoring systems. The framework for the approach is derived from minimax decision theory (minimum information approach), i.e. optimal rules are obtained by minimizing the maximum expected loss associated with each possible decision rule. The binomial model was assumed for the conditional probability of a correct response given the true level of functioning, whereas threshold loss was adopted for the loss function involved. A simple decision rule is given for which only the minimum true level of functioning required for being a ‘true master’ and the value of the loss ratio have to be specified in advance by the decision-maker. The procedures are demonstrated for the problem of determining the optimal number of interrogatory examples for concept-learning in the Minnesota Adaptive Instructional System (MAIS). The Bayesian decision component assumed in the MAIS and the minimax strategy are compared with each other in terms of their weak and strong points. An empirical example of determining the optimal number of interrogatory examples for concept-learning in medicine concludes the paper.