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.

翻译：本文研究了迭代机器教学（IMT）问题，其中教师向学习者逐步提供示例，以使学习者能够快速收敛到目标模型。然而，现有的IMT算法完全基于参数化的目标模型族，主要关注参数空间中的收敛性，导致当目标模型被定义为不依赖参数的函数时难以适用。为解决这一局限，我们研究了一个更通用的任务——非参数化迭代机器教学（NIMT），旨在以迭代方式向学习者教授非参数化目标模型。与仅在参数空间中操作的参数化IMT不同，我们将NIMT视为函数空间中的函数优化问题。为求解该问题，我们提出了随机式和贪婪式两种函数教学算法。在适当假设下，我们得到了随机教学算法的迭代教学维度（ITD），该维度作为NIMT中ITD的统一上界。此外，贪婪教学算法具有显著更低的ITD，达到了NIMT中ITD的更紧上界。最后，我们通过在非参数化场景下的大量实验验证了理论发现的正确性。