Learning from queries for maximum information gain in imperfectly learnable problems

In supervised learning, learning from queries rather than from random examples can improve generalization performance significantly. We study the performance of query learning for problems where the student cannot learn the teacher perfectly, which occur frequently in practice. As a prototypical scenario of this kind, we consider a linear perceptron student learning a binary perceptron teacher. Two kinds of queries for maximum information gain, i.e., minimum entropy, are investigated: Minimum student space entropy (MSSE) queries, which are appropriate if the teacher space is unknown, and minimum teacher space entropy (MTSE) queries, which can be used if the teacher space is assumed to be known, but a student of a simpler form has deliberately been chosen. We find that for MSSE queries, the structure of the student space determines the efficacy of query learning, whereas MTSE queries lead to a higher generalization error than random examples, due to a lack of feedback about the progress of the student in the way queries are selected.