  Machine teaching studies the interaction between a teacher and a
student/learner where the teacher selects training examples for the learner to
learn a specific task. The typical assumption is that the teacher has perfect
knowledge of the task---this knowledge comprises knowing the desired learning
target, having the exact task representation used by the learner, and knowing
the parameters capturing the learning dynamics of the learner. Inspired by
real-world applications of machine teaching in education, we consider the
setting where teacher's knowledge is limited and noisy, and the key research
question we study is the following: When does a teacher succeed or fail in
effectively teaching a learner using its imperfect knowledge? We answer this
question by showing connections to how imperfect knowledge affects the
teacher's solution of the corresponding machine teaching problem when
constructing optimal teaching sets. Our results have important implications for
designing robust teaching algorithms for real-world applications.
