License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2023.16
URN: urn:nbn:de:0030-drops-176689
URL: https://drops.dagstuhl.de/opus/volltexte/2023/17668/
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Bshouty, Nader H.

Non-Adaptive Proper Learning Polynomials

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LIPIcs-STACS-2023-16.pdf (0.7 MB)


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}
}

Keywords: Polynomial, Learning, Testing
Collection: 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)
Issue Date: 2023
Date of publication: 03.03.2023


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