# Nonparametric Iterative Machine Teaching

arXiv: https://arxiv.org/abs/2306.03007 · HTML: https://mlsanity.com/paper/2306.03007/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 83 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [Maximum Mean Discrepancy Gradient Flow](https://mlsanity.com/paper/1906.04370/) (2019)
- [Policy Teaching via Environment Poisoning: Training-time Adversarial Attacks against Reinforcement Learning](https://mlsanity.com/paper/2003.12909/) (2020)
- [Policy Poisoning in Batch Reinforcement Learning and Control](https://mlsanity.com/paper/1910.05821/) (2019)
- [An Overview of Machine Teaching](https://mlsanity.com/paper/1801.05927/) (2018)
- [Black-Box Certification with Randomized Smoothing: A Functional Optimization Based Framework](https://mlsanity.com/paper/2002.09169/) (2020)
- [Iterative Machine Teaching](https://mlsanity.com/paper/1705.10470/) (2017)
- [Near-Optimally Teaching the Crowd to Classify](https://mlsanity.com/paper/1402.2092/) (2014)
- [Fast Discrete Distribution Clustering Using Wasserstein Barycenter with Sparse Support](https://mlsanity.com/paper/1510.00012/) (2015)
- [Interactive Teaching Algorithms for Inverse Reinforcement Learning](https://mlsanity.com/paper/1905.11867/) (2019)
- [Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters](https://mlsanity.com/paper/1806.03915/) (2018)
- [Towards Black-box Iterative Machine Teaching](https://mlsanity.com/paper/1710.07742/) (2017)
- [The Teaching Dimension of Linear Learners](https://mlsanity.com/paper/1512.02181/) (2015)
- [Machine Teaching for Bayesian Learners in the Exponential Family](https://mlsanity.com/paper/1306.4947/) (2013)
- [Teaching Multiple Concepts to a Forgetful Learner](https://mlsanity.com/paper/1805.08322/) (2018)
- [Understanding the Role of Adaptivity in Machine Teaching: The Case of Version Space Learners](https://mlsanity.com/paper/1802.05190/) (2018)
- [Functional Gradient Boosting based on Residual Network Perception](https://mlsanity.com/paper/1802.09031/) (2018)
- [Preference-Based Batch and Sequential Teaching: Towards a Unified View of Models](https://mlsanity.com/paper/1910.10944/) (2019)
- [Unlearn What You Have Learned: Adaptive Crowd Teaching with Exponentially Decayed Memory Learners](https://mlsanity.com/paper/1804.06481/) (2018)
- [Machine Teaching of Active Sequential Learners](https://mlsanity.com/paper/1809.02869/) (2018)
- [An Optimal Control Approach to Sequential Machine Teaching](https://mlsanity.com/paper/1810.06175/) (2018)
- [Iterative Teaching by Label Synthesis](https://mlsanity.com/paper/2110.14432/) (2021)
- [Sinkhorn Barycenter via Functional Gradient Descent](https://mlsanity.com/paper/2007.10449/) (2020)

## Built on by (most cited first, 9 of 9)

- [Nonparametric Teaching of Implicit Neural Representations](https://mlsanity.com/paper/2405.10531/) (2024)
- [Imaging Interiors: An Implicit Solution to Electromagnetic Inverse Scattering Problems](https://mlsanity.com/paper/2407.09352/) (2024)
- [Nonparametric Teaching for Multiple Learners](https://mlsanity.com/paper/2311.10318/) (2023)
- [Nonparametric Teaching for Graph Property Learners](https://mlsanity.com/paper/2505.14170/) (2025)
- [Representational Alignment Supports Effective Machine Teaching](https://mlsanity.com/paper/2406.04302/) (2024)
- [NTK-Guided Implicit Neural Teaching](https://mlsanity.com/paper/2511.15487/) (2025)
- [Nonparametric Teaching of Attention Learners](https://mlsanity.com/paper/2602.20461/) (2026)
- [Large-Scale Bayesian Tensor Reconstruction via Approximate Message Passing](https://mlsanity.com/paper/2505.16305/) (2025)
- [Model Evolution Under Zeroth-Order Optimization: A Neural Tangent Kernel Perspective](https://mlsanity.com/paper/2603.21169/) (2026)

## Abstract (arXiv)

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.