We address the problem of learning preference relations on multi-attribute (or combinatorial) domains. We do so by making a very simple hypothesis about the dependence structure between attributes that the preference relation enjoys, namely separability (no preferential dependencies between attributes). Given a set of examples consisting of comparisons between alternatives, we want to output a separable CP-net, consisting of local preferences on each of the attributes, that fits the examples. We consider three forms of compatibility between a CP-net and a set of examples, and for each of them we give useful characterizations as well as complexity results. 1

Abstract—A conversational recommender system iteratively shows a small set of options for its user to choose between. In order to select these options, the system may analyze the queries tried by the user to derive whether one option is dominated by others with respect to the user’s preferences. This paper describes a framework for preference dominance. Two instances of the framework are developed for query suggestion in a conversational recommender system. The first instance of the framework is based on a basic quantitative preferences formalism, where products are compared using sums of weights of features. The second is a qualitative preference formalism, using a language that generalizes CP-nets, where models are a kind of generalized lexicographic order. A key feature of both methods is that deductions of preference dominance can be made efficiently, since this procedure needs to be applied for many pairs of products. We show that, by allowing the recommender to focus on undominated options, which are ones that the user is likely to be contemplating, both approaches can dramatically reduce the amount of advice the recommender needs to give to a user compared to what would be given by systems without this kind of reasoning. I.

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.

A conversational recommender system iteratively shows a small set of options for its user to choose between. In order to select these options, the system may analyze the queries tried by the user to derive whether one option is dominated by others with respect to the user’s preferences. The system can then suggest that the user try one of the undominated options, as they represent the best options in the light of the user preferences elicited so far. This paper describes a framework for preference dominance. Two instances of the framework are developed for query suggestion in a conversational recommender system. The first instance of the framework is based on a basic quantitative preferences formalism, where options are compared using sums of weights of their features. The second is a qualitative preference formalism, using a language that generalises CP-nets, where models are a kind of generalised lexicographic order. A key feature of both methods is that deductions of preference dominance can be made efficiently, since 1 April 12, 2011 20:45 WSPC/INSTRUCTION FILE ijait2011-twbr 2 this procedure needs to be applied for many pairs of options. We show that, by allowing the recommender to focus on undominated options, which are ones that the user is likely to be contemplating, both approaches can dramatically reduce the amount of advice the recommender needs to give to a user compared to what would be given by systems without this kind of reasoning. 1.