Being taught can be faster than asking questions
Ronald L. Rivest, Yiqun Lisa Yin · 1995
We explore the power of teaChillg by StUdyiIlg two uu-lille learuing models: teach er-clirecteci learninE and self-dlrectecl learning. In both models, the learner tries to identify an unkuowu concept based on examples of the concept presented one at, a time. The learner predirts wheth~r each example is positive or negative with immediate feedback, and the ol)ject,ive is to minimize the uurnl)er of predict,iou mistakes. ThP examples are selected by the teacher in teacher-dlrectecl learning and hy tlhe learner itself in self-directed learning. R,oughly, teacher-directed learning represents the scenario in which a teacher teaches a class of learners, and self-directed learning represents the scenario in which a smart learnerasks questious and learns by itself. For all previolmly studied concept classes, the rnirrimum numl)er of mistalws in teacller-ciirectf ecl learning is always larger than that, in self-directed learning. This raises an mtermting question [.)t ’ whrt, hrr teaching is helpful for all learners mrlu(ling the smart learner’. Assuming the existence of clue-way functioms, we construct com cept clahses for which the miuimum nurnher of mislakes is hnear in teacher-directed learning I,ut sllI>rrlJolyllorlllal m self-directed learning, cler~lc~llst,rt~tillg the power of a helpful teacher in a Iearmng process.