Almost Optimal Proper Learning and Testing Polynomials

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We give the first almost optimal polynomial-time proper learning algorithm of Boolean sparse multivariate polynomial under the uniform distribution. For s-sparse polynomial over n variables and ϵ= 1 / sβ, β> 1, our algorithm makes (formula presetend) qU=(sϵ)logββ+O(1β)+O~(s)(log1ϵ)logn queries. Notice that our query complexity is sublinear in 1 / ϵ and almost linear in s. All previous algorithms have query complexity at least quadratic in s and linear in 1 / ϵ. We then prove the almost tight lower bound (formula presented) qL=(sϵ)logββ+Ω(1β)+Ω(s)(log1ϵ)logn, Applying the reduction in [9] with the above algorithm, we give the first almost optimal polynomial-time tester for s-sparse polynomial. Our tester, for β> 3.404, makes(formula presentes)O~(sϵ) queries.

Original languageEnglish
Title of host publicationLATIN 2022
Subtitle of host publicationTheoretical Informatics - 15th Latin American Symposium, 2022, Proceedings
EditorsArmando Castañeda, Francisco Rodríguez-Henríquez
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages16
ISBN (Print)9783031206238
StatePublished - 2022
Event15th Latin American Symposium on Theoretical Informatics, LATIN 2022 - Guanajuato, Mexico
Duration: 7 Nov 202211 Nov 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13568 LNCS


Conference15th Latin American Symposium on Theoretical Informatics, LATIN 2022


  • Polynomial
  • Proper learning
  • Property testing

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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