  Given a sequential learning algorithm and a target model, sequential machine
teaching aims to find the shortest training sequence to drive the learning
algorithm to the target model. We present the first principled way to find such
shortest training sequences. Our key insight is to formulate sequential machine
teaching as a time-optimal control problem. This allows us to solve sequential
teaching by leveraging key theoretical and computational tools developed over
the past 60 years in the optimal control community. Specifically, we study the
Pontryagin Maximum Principle, which yields a necessary condition for optimality
of a training sequence. We present analytic, structural, and numerical
implications of this approach on a case study with a least-squares loss
function and gradient descent learner. We compute optimal training sequences
for this problem, and although the sequences seem circuitous, we find that they
can vastly outperform the best available heuristics for generating training
sequences.
