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Preference Learning pp 273–296Cite as

Learning Ordinal Preferences on Multiattribute Domains: The Case of CP-nets

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Abstract

A recurrent issue in decision making is to extract a preference structure by observing the user’s behavior in different situations. In this paper, we investigate the problem of learning ordinal preference orderings over discrete multiattribute, or combinatorial, domains. Specifically, we focus on the learnability issue of conditional preference networks, or CP-nets, that have recently emerged as a popular graphical language for representing ordinal preferences in a concise and intuitive manner. This paper provides results in both passive and active learning. In the passive setting, the learner aims at finding a CP-net compatible with a supplied set of examples, while in the active setting the learner searches for the cheapest interaction policy with the user for acquiring the target CP-net.

Partially supported by the ANR projects CANAR (ANR-06-BLAN-0383-02) and PHAC (ANR-05-BLAN-0384-01

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Notes

  1. 1.

    If we want to do this, we have to resort to a more expressive language such as TCP-nets [6] or conditional preference theories [31].

  2. 2.

    Note that 𝒯 is both weakly separable and does not contain any cycles as it was the case for Example 4, yet is not strongly separable.

  3. 3.

    Such a translation exists for strong separability (which we do not give here), but unfortunately, the set of clauses generated uses \(\mathcal{O}({n}^{2})\) variables (where n is the set of examples), which limits its practical applicability.

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Authors and Affiliations

  1. LAMSADE, Université Paris-Dauphine, CNRS, Paris, France

    Yann Chevaleyre & Jérôme Lang

  2. LIRMM, Université Montpellier II, CNRS, Montpellier, France

    Frédéric Koriche

  3. IRIT, Université Paul Sabatier, CNRS, Toulouse, France

    Jérôme Mengin

  4. GREYC, Université de Caen Basse-Normandie, CNRS, ENSICAEN, Basse-Normandie, France

    Bruno Zanuttini

Authors
  1. Yann Chevaleyre
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  2. Frédéric Koriche
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  3. Jérôme Lang
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  4. Jérôme Mengin
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  5. Bruno Zanuttini
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Correspondence to Yann Chevaleyre .

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Editors and Affiliations

  1. FB Informatik, TU Darmstadt, Hochschulstr. 10, Darmstadt, 64289, Germany

    Johannes Fürnkranz

  2. FB Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Str., Marburg, 35032, Germany

    Eyke Hüllermeier

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Chevaleyre, Y., Koriche, F., Lang, J., Mengin, J., Zanuttini, B. (2010). Learning Ordinal Preferences on Multiattribute Domains: The Case of CP-nets. In: Fürnkranz, J., Hüllermeier, E. (eds) Preference Learning. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14125-6_13

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  • DOI: https://doi.org/10.1007/978-3-642-14125-6_13

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