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：本文研究迭代式机器教学（IMT）问题，其中教师逐步向学习者提供示例，使学习者能够快速收敛至目标模型。然而，现有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存在困难。为解决该局限性，我们研究更通用的任务——非参数迭代式机器教学（NIMT），旨在以迭代方式向学习者传授非参数目标模型。不同于仅在参数空间操作的参数化IMT，我们将NIMT建模为函数空间中的泛函优化问题。为此，我们提出随机与贪婪两种函数教学算法。在合理假设下，我们推导出随机教学算法的迭代教学维度（ITD），该值可作为NIMT中ITD的统一上界。进一步地，贪婪教学算法具有显著更低的ITD，达到NIMT中更紧致的ITD上界。最后，通过非参数场景的大量实验验证了理论发现的正确性。