Abstract
We give the first polynomial-time non-adaptive proper learning algorithm of Boolean sparse multivariate polynomial under the uniform distribution. Our algorithm, for s-sparse polynomial over n variables, makes q = (s/ε)^{γ(s,ε)}log n queries where 2.66 ≤ γ(s,ε) ≤ 6.922 and runs in Õ(n)⋅ poly(s,1/ε) time. We also show that for any ε = 1/s^{O(1)} any non-adaptive learning algorithm must make at least (s/ε)^{Ω(1)}log n queries. Therefore, the query complexity of our algorithm is also polynomial in the optimal query complexity and optimal in n.
BibTeX - Entry
@InProceedings{bshouty:LIPIcs.STACS.2023.16,
author = {Bshouty, Nader H.},
title = {{Non-Adaptive Proper Learning Polynomials}},
booktitle = {40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
pages = {16:1--16:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-266-2},
ISSN = {1868-8969},
year = {2023},
volume = {254},
editor = {Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/17668},
URN = {urn:nbn:de:0030-drops-176689},
doi = {10.4230/LIPIcs.STACS.2023.16},
annote = {Keywords: Polynomial, Learning, Testing}
}
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Keywords: |
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Polynomial, Learning, Testing |
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Collection: |
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40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023) |
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Issue Date: |
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2023 |
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Date of publication: |
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03.03.2023 |
Creative Commons Attribution 4.0 International license (CC BY 4.0)