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Barrier Certificates for Assured Machine Teaching

Ahmadi, Mohamadreza and Wu, Bo and Chen, Yuxin and Yue, Yisong and Topcu, Ufuk (2019) Barrier Certificates for Assured Machine Teaching. In: 2019 American Control Conference (ACC). IEEE , Piscataway, NJ, pp. 3658-3663. ISBN 978-1-5386-7926-5. https://resolver.caltech.edu/CaltechAUTHORS:20190205-102249789

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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.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://ieeexplore.ieee.org/document/8815376PublisherArticle
https://arxiv.org/abs/1810.00093arXivDiscussion Paper
ORCID:
AuthorORCID
Ahmadi, Mohamadreza0000-0003-1447-3012
Yue, Yisong0000-0001-9127-1989
Additional Information:© 2019 AACC. This work was supported by AFOSR FA9550-19-1-0005, DARPA D19AP00004, NSF 1646522 and NSF 1652113.
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-19-1-0005
Defense Advanced Research Projects Agency (DARPA)D19AP00004
NSFCNS-1646522
NSFCNS-1652113
DOI:10.48550/arXiv.1810.00093
Record Number:CaltechAUTHORS:20190205-102249789
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190205-102249789
Official Citation:M. Ahmadi, B. Wu, Y. Chen, Y. Yue and U. Topcu, "Barrier Certificates for Assured Machine Teaching," 2019 American Control Conference (ACC), Philadelphia, PA, USA, 2019, pp. 3658-3663. URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8815376&isnumber=8814292
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92662
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Feb 2019 19:03
Last Modified:02 Jun 2023 00:42

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