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Learning Boolean Halfspaces with Small Weights from Membership Queries

  • Conference paper
Algorithmic Learning Theory (ALT 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8776))

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Abstract

We consider the problem of proper learning a Boolean Halfspace with integer weights {0,1,…,t} from membership queries only. The best known algorithm for this problem is an adaptive algorithm that asks \(n^{O(t^5)}\) membership queries where the best lower bound for the number of membership queries is n t [4].

In this paper we close this gap and give an adaptive proper learning algorithm with two rounds that asks n O(t) membership queries. We also give a non-adaptive proper learning algorithm that asks \(n^{O(t^3)}\) membership queries.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Technion, Haifa, Israel

    Hasan Abasi & Nader H. Bshouty

  2. Convent of Nazareth School, Grade 11, Abas 7, Haifa, Israel

    Ali Z. Abdi

Authors
  1. Hasan Abasi
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  2. Ali Z. Abdi
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  3. Nader H. Bshouty
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Editor information

Editors and Affiliations

  1. Montanuniversitaet Leoben, 8700, Leoben, Austria

    Peter Auer

  2. Department of Philosophy, King’s College, WC2R 2LS, London, UK

    Alexander Clark

  3. Division of Computer Science, Hokkaido University, N-14, W-9, 060-0814, Sapporo, Japan

    Thomas Zeugmann

  4. Department of Computer Science, University of Regina, S4S 0A2, Regina, SK, Canada

    Sandra Zilles

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© 2014 Springer International Publishing Switzerland

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Abasi, H., Abdi, A.Z., Bshouty, N.H. (2014). Learning Boolean Halfspaces with Small Weights from Membership Queries. In: Auer, P., Clark, A., Zeugmann, T., Zilles, S. (eds) Algorithmic Learning Theory. ALT 2014. Lecture Notes in Computer Science(), vol 8776. Springer, Cham. https://doi.org/10.1007/978-3-319-11662-4_8

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  • DOI: https://doi.org/10.1007/978-3-319-11662-4_8

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11661-7

  • Online ISBN: 978-3-319-11662-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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