Barrier Certificates for Assured Machine Teaching
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 wellestablished 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 preferencebased 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 discretetime switched system. Subsequently, we use barrier certificates to verify settheoric 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 sumofsquares (SOS) program. For illustration, we show how the proposed framework based on control theory can be used to verify the teaching performance of two wellknown machine teaching methods.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1810.00093
 Bibcode:
 2018arXiv181000093A
 Keywords:

 Electrical Engineering and Systems Science  Systems and Control