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 | ||||||||||
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Additional Information: | © 2019 AACC. This work was supported by AFOSR FA9550-19-1-0005, DARPA D19AP00004, NSF 1646522 and NSF 1652113. | ||||||||||
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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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