We investigate the problem of eliciting CP-nets in the well-known model of exact learning with equivalence and membership queries. The goal is to identify a preference ordering with a binary-valued CP-net by guiding the user through a sequence of queries. Each example is a dominance test on some pair of outcomes. In this setting, we show that acyclic CP-nets are not learnable with equivalence queries alone, while they are learnable with the help of membership queries if the supplied examples are restricted to swaps. A similar property holds for tree CP-nets with arbitrary examples. In fact, membership queries allow us to provide attributeefficient algorithms for which the query complexity is only logarithmic in the number of attributes. Such results highlight the utility of this model for eliciting CP-nets in large multi-attribute domains. 1

various classes of models of lexicographic orderings

A recurrent issue in automated decision making is to extract a preference structure from a set of examples. In this paper, we investigate the problem of learning ordinal preference orderings over discrete multi-attribute, or combinatorial, domains. Specifically, we concentrate 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 passive learning, the learner aims at finding a CP-net compatible with a given set of examples, while in active learning the learner searches for the cheapest interaction policy with the user for acquiring the target CP-net.

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