Non-Adaptive Proper Learning Polynomials

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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/sO(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.

Original languageEnglish
Title of host publication40th International Symposium on Theoretical Aspects of Computer Science, STACS 2023
EditorsPetra Berenbrink, Patricia Bouyer, Anuj Dawar, Mamadou Moustapha Kante
ISBN (Electronic)9783959772662
DOIs
StatePublished - 1 Mar 2023
Event40th International Symposium on Theoretical Aspects of Computer Science, STACS 2023 - Hamburg, Germany
Duration: 7 Mar 20239 Mar 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume254

Conference

Conference40th International Symposium on Theoretical Aspects of Computer Science, STACS 2023
Country/TerritoryGermany
CityHamburg
Period7/03/239/03/23

Keywords

  • Learning
  • Polynomial
  • Testing

All Science Journal Classification (ASJC) codes

  • Software

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