  We study the problem of active learning with the added twist that the learner
is assisted by a helpful teacher. We consider the following natural interaction
protocol: At each round, the learner proposes a query asking for the label of
an instance $x^q$, the teacher provides the requested label $\{x^q, y^q\}$
along with explanatory information to guide the learning process. In this
paper, we view this information in the form of an additional contrastive
example ($\{x^c, y^c\}$) where $x^c$ is picked from a set constrained by $x^q$
(e.g., dissimilar instances with the same label). Our focus is to design a
teaching algorithm that can provide an informative sequence of contrastive
examples to the learner to speed up the learning process. We show that this
leads to a challenging sequence optimization problem where the algorithm's
choices at a given round depend on the history of interactions. We investigate
an efficient teaching algorithm that adaptively picks these contrastive
examples. We derive strong performance guarantees for our algorithm based on
two problem-dependent parameters and further show that for specific types of
active learners (e.g., a generalized binary search learner), the proposed
teaching algorithm exhibits strong approximation guarantees. Finally, we
illustrate our bounds and demonstrate the effectiveness of our teaching
framework via two numerical case studies.
