Barrier Certificates for Assured Machine Teaching

TL;DR

This paper introduces a control-theoretic framework using barrier certificates to verify and guarantee the performance of machine teaching algorithms modeled as hybrid systems, ensuring reliable teaching strategies.

Contribution

It formulates machine teaching as a hybrid system and applies barrier certificates with SOS programming to verify teaching guarantees, a novel control-theoretic approach.

Findings

Barrier certificates can verify teaching performance.

The framework applies to preference-based learners.

Numerical methods enable practical verification.

Abstract

Machine teaching can be viewed as optimal control for learning. Given a learner's model, machine teaching aims to determine the optimal training data to steer the learner towards a target hypothesis. In this paper, we are interested in providing assurances for machine teaching algorithms using control theory. In particular, we study a well-established learner's model in the machine teaching literature that is captured by the local preference over a version space. We interpret the problem of teaching a preference-based learner as solving a partially observable Markov decision process (POMDP). We then show that the POMDP formulation can be cast as a special hybrid system, i.e., a discrete-time switched system. Subsequently, we use barrier certificates to verify set-theoric properties of this special hybrid system. We show how the computation of the barrier certificate can be decomposed and numerically implemented as the solution to a sum-of-squares (SOS) program. For illustration, we show how the proposed framework based on control theory can be used to verify the teaching performance of two well-known machine teaching methods.