  Machine teaching can be viewed as optimal control for learning. Given a
learner's model, machine teaching aims to determine the optimal training data
to steer the learner towards a target hypothesis. In this paper, we are
interested in providing assurances for machine teaching algorithms using
control theory. In particular, we study a well-established learner's model in
the machine teaching literature that is captured by the local preference over a
version space. We interpret the problem of teaching a preference-based learner
as solving a partially observable Markov decision process (POMDP). We then show
that the POMDP formulation can be cast as a special hybrid system, i.e., a
discrete-time switched system. Subsequently, we use barrier certificates to
verify set-theoric properties of this special hybrid system. We show how the
computation of the barrier certificate can be decomposed and numerically
implemented as the solution to a sum-of-squares (SOS) program. For
illustration, we show how the proposed framework based on control theory can be
used to verify the teaching performance of two well-known machine teaching
methods.
