An Optimal Control Approach to Sequential Machine Teaching
Laurent Lessard, Xuezhou Zhang, Xiaojin Zhu
Abstract
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 opti- mality of a training sequence. We present analytic, structural, and numerical implica- tions of this approach on a case study with a least-squares loss function and gradient de- scent learner. We compute optimal train- ing 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.
BibTeX
@InProceedings{pmlr-v89-lessard19a,
title = {An Optimal Control Approach to Sequential Machine Teaching},
author = {Lessard, Laurent and Zhang, Xuezhou and Zhu, Xiaojin},
booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics},
pages = {2495--2503},
year = {2019},
editor = {Chaudhuri, Kamalika and Sugiyama, Masashi},
volume = {89},
series = {Proceedings of Machine Learning Research},
month = {16--18 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v89/lessard19a/lessard19a.pdf},
url = {https://proceedings.mlr.press/v89/lessard19a.html},
abstract = {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 opti- mality of a training sequence. We present analytic, structural, and numerical implica- tions of this approach on a case study with a least-squares loss function and gradient de- scent learner. We compute optimal train- ing 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.}
}