  In this paper, we consider the problem of Iterative Machine Teaching (IMT),
where the teacher provides examples to the learner iteratively such that the
learner can achieve fast convergence to a target model. However, existing IMT
algorithms are solely based on parameterized families of target models. They
mainly focus on convergence in the parameter space, resulting in difficulty
when the target models are defined to be functions without dependency on
parameters. To address such a limitation, we study a more general task --
Nonparametric Iterative Machine Teaching (NIMT), which aims to teach
nonparametric target models to learners in an iterative fashion. Unlike
parametric IMT that merely operates in the parameter space, we cast NIMT as a
functional optimization problem in the function space. To solve it, we propose
both random and greedy functional teaching algorithms. We obtain the iterative
teaching dimension (ITD) of the random teaching algorithm under proper
assumptions, which serves as a uniform upper bound of ITD in NIMT. Further, the
greedy teaching algorithm has a significantly lower ITD, which reaches a
tighter upper bound of ITD in NIMT. Finally, we verify the correctness of our
theoretical findings with extensive experiments in nonparametric scenarios.
