# An Optimal Control Approach to Sequential Machine Teaching

arXiv: https://arxiv.org/abs/1810.06175 · HTML: https://mlsanity.com/paper/1810.06175/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2018.

## Built on by (most cited first, 11 of 11)

- [Teaching an Active Learner with Contrastive Examples](https://mlsanity.com/paper/2110.14888/) (2021)
- [Accumulative Poisoning Attacks on Real-time Data](https://mlsanity.com/paper/2106.09993/) (2021)
- [Iterative Teaching by Label Synthesis](https://mlsanity.com/paper/2110.14432/) (2021)
- [Nonparametric Iterative Machine Teaching](https://mlsanity.com/paper/2306.03007/) (2023)
- [Iterative Teaching by Data Hallucination](https://mlsanity.com/paper/2210.17467/) (2022)
- [Iterative Teacher-Aware Learning](https://mlsanity.com/paper/2110.00137/) (2021)
- [Nonparametric Teaching for Multiple Learners](https://mlsanity.com/paper/2311.10318/) (2023)
- [Representational Alignment Supports Effective Machine Teaching](https://mlsanity.com/paper/2406.04302/) (2024)
- [Distribution Matching for Machine Teaching](https://mlsanity.com/paper/2105.13809/) (2021)
- [One-shot Machine Teaching: Cost Very Few Examples to Converge Faster](https://mlsanity.com/paper/2212.06416/) (2022)
- [Attacks on Online Learners: a Teacher-Student Analysis](https://mlsanity.com/paper/2305.11132/) (2023)

## Abstract (arXiv)

Given a sequential learning algorithm and a target model, sequential machine teaching aims to find the shortest training sequence to drive the learning algorithm to the target model. We present the first principled way to find such shortest training sequences. Our key insight is to formulate sequential machine teaching as a time-optimal control problem. This allows us to solve sequential teaching by leveraging key theoretical and computational tools developed over the past 60 years in the optimal control community. Specifically, we study the Pontryagin Maximum Principle, which yields a necessary condition for optimality of a training sequence. We present analytic, structural, and numerical implications of this approach on a case study with a least-squares loss function and gradient descent learner. We compute optimal training sequences for this problem, and although the sequences seem circuitous, we find that they can vastly outperform the best available heuristics for generating training sequences.