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Submodular Learning and Covering with Response-Dependent Costs

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Algorithmic Learning Theory (ALT 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9925))

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Abstract

We consider interactive learning and covering problems, in a setting where actions may incur different costs, depending on the response to the action. We propose a natural greedy algorithm for response-dependent costs. We bound the approximation factor of this greedy algorithm in active learning settings as well as in the general setting. We show that a different property of the cost function controls the approximation factor in each of these scenarios. We further show that in both settings, the approximation factor of this greedy algorithm is near-optimal among all greedy algorithms. Experiments demonstrate the advantages of the proposed algorithm in the response-dependent cost setting.

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Notes

  1. 1.

    We may assume without loss of generality that \(u(x,S) = 0\) whenever \((x,y) \in S\).

  2. 2.

    http://snap.stanford.edu/data/egonets-Facebook.html.

  3. 3.

    http://snap.stanford.edu/data/ca-GrQc.html.

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Acknowledgements

This work was supported in part by the Israel Science Foundation (grant No. 555/15).

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Authors and Affiliations

  1. Ben-Gurion University of the Negev, Beersheba, Israel

    Sivan Sabato

Authors
  1. Sivan Sabato
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Correspondence to Sivan Sabato .

Editor information

Editors and Affiliations

  1. Montanuniversität Leoben , Leoben, Austria

    Ronald Ortner

  2. Ruhr-Uni-Bochum , Bochum, Germany

    Hans Ulrich Simon

  3. University of Regina , Regina, Saskatchewan, Canada

    Sandra Zilles

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Sabato, S. (2016). Submodular Learning and Covering with Response-Dependent Costs. In: Ortner, R., Simon, H., Zilles, S. (eds) Algorithmic Learning Theory. ALT 2016. Lecture Notes in Computer Science(), vol 9925. Springer, Cham. https://doi.org/10.1007/978-3-319-46379-7_9

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  • DOI: https://doi.org/10.1007/978-3-319-46379-7_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46378-0

  • Online ISBN: 978-3-319-46379-7

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