Peter Sollich, David Saad
In supervised learning, learning from queries rather than from random examples can improve generalization performance signif(cid:173) icantly. 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 en(cid:173) tropy (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 deter(cid:173) mines 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.