  In sequential machine teaching, a teacher's objective is to provide the
optimal sequence of inputs to sequential learners in order to guide them
towards the best model. In this paper we extend this setting from current
static one-data-set analyses to learners which change their learning algorithm
or latent state to improve during learning, and to generalize to new datasets.
We introduce a multi-agent formulation in which learners' inner state may
change with the teaching interaction, which affects the learning performance in
future tasks. In order to teach such learners, we propose an optimal control
approach that takes the future performance of the learner after teaching into
account. This provides tools for modelling learners having inner states, and
machine teaching of meta-learning algorithms. Furthermore, we distinguish
manipulative teaching, which can be done by effectively hiding data and also
used for indoctrination, from more general education which aims to help the
learner become better at generalization and learning in new datasets in the
absence of a teacher.
