  Like many problems in AI in their general form, supervised learning is
computationally intractable. We hypothesize that an important reason humans can
learn highly complex and varied concepts, in spite of the computational
difficulty, is that they benefit tremendously from experienced and insightful
teachers. This paper proposes a new learning framework that provides a role for
a knowledgeable, benevolent teacher to guide the process of learning a target
concept in a series of "curricular" phases or rounds. In each round, the
teacher's role is to act as a moderator, exposing the learner to a subset of
the available training data to move it closer to mastering the target concept.
Via both theoretical and empirical evidence, we argue that this framework
enables simple, efficient learners to acquire very complex concepts from
examples. In particular, we provide multiple examples of concept classes that
are known to be unlearnable in the standard PAC setting along with provably
efficient algorithms for learning them in our extended setting. A key focus of
our work is the ability to learn complex concepts on top of simpler, previously
learned, concepts---a direction with the potential of creating more competent
artificial agents.
