Teaching Dimensions Based on Cooperative Learning

Abstract

The problem of how a teacher and a learner can cooperate in the process of learning concepts from examples in order to minimize the required sample size without "coding tricks" has been widely addressed, yet without achieving teaching and learning protocols that meet what seems intuitively an optimal choice for selecting samples in teaching. We introduce the model of subset teaching sets, based on the idea that both teacher and learner can exploit the assumption that the partner is cooperative. We show how this can reduce the sample size drastically without using coding tricks. For instance, monomials can be taught with only two examples independent of the number of variables. The corresponding variant of the teaching dimension (STD) turns out to be nonmonotonic with respect to subclasses of concept classes. We discuss why this nonmonotonicity might be inherent in optimal cooperative teaching scenarios. Nevertheless, trying to overcome nonmonotonicity, we introduce a second variant, the recursive teaching dimension (RTD), which is monotonic and yields the same positive results for some concept classes, such as the class of all monomials, yet can be arbitrarily worse than the STD.