Exact learning via teaching assistants (extended abstract)

In continuation of our earlier paper [3], we study in detail the teaching assistant model of exact learning. In [3] we show that the exact learnability of some algebraic concept classes can be more sharply classified in this model than in Angluin's model. The teaching assistant model can be seen as an enhancement of Angluin's model. The new ingredient is that apart from the learner and teacher there is a third agent called teaching assistant which acts as an intermediary between the learner and teacher. In this paper we investigate in detail the learnability of various concept classes in the teaching assistant model. After giving the precise definition of the model, we first discuss the possibility of precisely capturing Angluin's model in the teaching assistant model and prove that this is not possible. We then discuss in detail the power of NP boolean AND co-NP and UP boolean AND co-UP assistants. Using machine characterizations of learnability with NP boolean AND co-NP and UP boolean AND co-UP assistants, we show that, information theoretically NP boolean AND co-NP and UP boolean AND co-UP assistants have the same power. We generalize the notion of teaching dimension [9] and define a notion of weak teaching dimension using which we characterize concept classes that are learnable with NP boolean AND co-NP assistants. Finally, with some algebraic concept classes as examples we obtain several separations between the power of various teaching assistant classes.