Abstract:
We explore the power of teaching by studying two on-line learning models: teacher-directed learning and self-directed learning. In both models, the learner tries to identify an unknown concept based on examples of the concept presented one at a time. The learner predicts whether each example is positive or negative with immediate feedback, and the objective is to minimize the number of prediction mistakes. The examples are selected by the teacher in teacher-directed learning and by the learner itself in self-directed learning. Roughly, 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 learner asks questions and learns by itself. For all previously studied concept classes, the minimum number of mistakes in teacher-directed learning is always larger than that in self-directed learning. This raises an interesting question of whether teaching is helpful for all learners including the smart learner. Assuming the existence of one-way functions, we construct concept classes for which the minimum number of mistakes is linear in teacher-directed learning
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