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Exact Learning Algorithms, Betting Games, and Circuit Lower Bounds

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Automata, Languages and Programming (ICALP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6755))

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Abstract

This paper extends and improves work of Fortnow and Klivans [5], who showed that if a circuit class \(\mathcal{C}\) has an efficient learning algorithm in Angluin’s model of exact learning via equivalence and membership queries [2], then we have the lower bound EXP NP \(\not\subseteq \mathcal{C}\). We use entirely different techniques involving betting games [4] to remove the NP oracle and improve the lower bound to EXP \(\not\subseteq \mathcal{C}\). This shows that it is even more difficult to design a learning algorithm for \(\mathcal{C}\) than the results of Fortnow and Klivans indicated.

This research was supported in part by NSF grants 0652601 and 0917417 and by an NWO travel grant. Part of this research was done while Hitchcock was on sabbatical at CWI.

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Authors and Affiliations

  1. Department of Computer Science, University of Wyoming, USA

    Ryan C. Harkins & John M. Hitchcock

Authors
  1. Ryan C. Harkins
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  2. John M. Hitchcock
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Editor information

Editors and Affiliations

  1. ICE-TCS, School of Computer Science, Reykjavik University, Menntavegur 1, IS 101, Reykjavik, Iceland

    Luca Aceto

  2. Fakultät für Informatik, Universität Wien, Universitätsstraße10/9, 1090, Wien, Österreich, Austria

    Monika Henzinger

  3. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czech Republic

    Jiří Sgall

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© 2011 Springer-Verlag Berlin Heidelberg

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Harkins, R.C., Hitchcock, J.M. (2011). Exact Learning Algorithms, Betting Games, and Circuit Lower Bounds. In: Aceto, L., Henzinger, M., Sgall, J. (eds) Automata, Languages and Programming. ICALP 2011. Lecture Notes in Computer Science, vol 6755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22006-7_35

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  • DOI: https://doi.org/10.1007/978-3-642-22006-7_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22005-0

  • Online ISBN: 978-3-642-22006-7

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