An Optimal Control Approach to Sequential Machine Teaching

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 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.

References in corpus (3)

• Poisoning Attacks against Support Vector Machines
• Optimization-Based Autonomous Racing of 1:43 Scale RC Cars
• Iterative Machine Teaching

Cited by in corpus (5)

• Online Data Poisoning Attack
• Using Machine Teaching to Investigate Human Assumptions when Teaching Reinforcement Learners
• NLOptControl: A modeling language for solving optimal control problems
• An Investigation of Data Poisoning Defenses for Online Learning
• The Sample Complexity of Teaching-by-Reinforcement on Q-Learning