Procédure de vote parallèle dans les référendums multiples : une approche expérimentale

Session "Articles"National audienceLes référendums multiples consistent à prendre une décision commune sur chacune d'un ensemble de questions binaires, à partir des préférences d'un ensemble de votants. Demander aux votants leur avis sur toutes les combinaisons de valeurs est pratiquement infaisable, en raison du nombre exponentiellement grand de ces combinaisons ; d'un autre côté, effectuer des votes en parallèle sur chacune des questions peut mener à des résultats fortement paradoxaux. Dans cet article, nous essayons de mesurer à quel point il est sous-optimal de procéder à un tel vote parallèle, en fonction de la règle de vote que l'on veut implémenter, et de la nature des préférences des votants (arbitraires, faiblement séparables ou fortement séparables). Nous utilisons pour cela une expérimentation sur des données generées aléatoirement

Apprentissage de CP-nets probabilistes

National audienceNous présentons une extension probabiliste des réseaux de préférences conditionnelles (CP-nets). Nous montrons comment ce formalisme permet d'apprendre de façon approximative les préférences d'un ensemble d'utilisateurs sur des objets définis de façon combinatoire. Notre approche utilise un algorithme de type expectation-maximisation

Learning Probabilistic CP-nets from Observations of Optimal Items

International audienceModelling preferences has been an active research topic in Artificial Intelligence for more than fifteen years. Existing formalisms are rich and flexible enough to describe the behaviour of complex decision rules. However, for being interesting in practice, these formalisms must also permit fast elicitation of a user's preferences, involving a reasonable amount of interaction only. Therefore, it is interesting to learn not a single model, but a probabilistic model that can compactly represent the preferences of a group of users - this model can then be finely tuned to fit one particular user. Even in contexts where a user is not anonymous, her preferences are usually ill-known, because they can depend on the value of non controllable state variable. In such contexts, we would like to be able to answer questions like "What is the probability that o is preferred to o' by some (unknown) agent?", or "Which item is most likely to be the preferred one, given some constraints?". We study in this paper how Probabilistic Conditional Preference networks can be learnt, both in off-line and on-line settings. We suppose that we have a list of items which, it is assumed, are or have been optimal for some user or in some context. Such a list can be, for instance, a list of items that have been sold. We prove that such information is sufficient to learn a partial order over the set of possible items, when these have a combinatorial structure

Probabilistic Conditional Preference Networks (JIAF 2013)

International audienceIn order to represent the preferences of a group of individuals, we introduce Probabilistic CP-nets (PCP-nets). PCP-nets provide a compact language for representing probability distributions over preference orderings. We argue that they are useful for aggregating preferences or modelling noisy preferences. Then we give efficient algorithms for the main reasoning problems, namely for computing the probability that a given outcome is preferred to another one, and the probability that a given outcome is optimal. As a by-product, we obtain an unexpected linear-time algorithm for checking dominance in a standard, tree-structured CP-net.Afin de représenter les préférences d’un groupe d’individus, nous introduisons les CP-nets probabilistes (PCP-net). Les PCP-nets fournissent un langage compact pour représenter des distributions de probabilités sur des ordres de préférences. Nous pensons qu’ils sont utiles pour modéliser des agrégations de préférences ou encore des préférences bruitées. Puis, nous proposons des algorithmes efficaces pour les principaux problèmes de raisonnement ; par exemple pour calculer la probabilité qu’un objet donné est préféré `a un autre, ou encore la probabilité qu’un objet donné est optimal. En tant que résultat dérivé, on obtient un algorithme, en temps linéaire inattendu, de contrôle de la dominance pour une structure arborescente

Probabilistic Conditional Preference Networks (UAI 2013)

International audienceThis paper proposes a \probabilistic" extension of conditional preference networks as a way to compactly represent a probability distributions over preference orderings. It studies the probabilistic counterparts of the main reasoning tasks, namely dominance testing and optimisation from the algorithmical and complexity viewpoints. Efficient algorithms for tree-structured probabilistic CP-nets are given. As a by-product we obtain a lineartime algorithm for dominance testing in standard, tree-structured CP-nets

Apprentissage de GAI-décompositions

National audienceDans cet article, nous étudions l'acquisition de GAI- décompositions de degré connu d'ordres de préférence dont un ensemble d'exemples est donné en entrée. Nous montrons que l'on peut représenter les GAI- décompositions cohérentes avec un ensemble d'exemples comme les solutions d'un système d'équations linéaires. Nous en déduisons un algorithme d'apprentissage passif (utilisant seulement des exemples observés) pour les GAI-décompositions de degré connu et constant. Nous montrons enfin comment généraliser ce résultat pour calculer des GAI-décompositions de degré ou de taille minimaux

Using and Learning GAI-Decompositions for Representing Ordinal Rankings

International audienceWe study the use of GAI-decomposable utility functions for representing ordinal rankings on combinatorial sets of objects. Considering only the relative order of objects leaves a lot of freedom for choosing a particular utility function, which allows one to get more compact representations. We focus on the problem of learning such representations, and give a polynomial PAC-learner for the case when a constant bound is known on the degree of the target representation. We also propose linear programming approaches for minimizing such representations

Learning Lexicographic Preference Trees From Positive Examples

This paper considers the task of learning the preferences of users on a combinatorial set of alternatives, as it can be the case for example with online configurators. In many settings, what is available to the learner is a set of positive examples of alternatives that have been selected during past interactions. We propose to learn a model of the users' preferences that ranks previously chosen alternatives as high as possible. In this paper, we study the particular task of learning conditional lexicographic preferences. We present an algorithm to learn several classes of lexicographic preference trees, prove convergence properties of the algorithm, and experiment on both synthetic data and on a real-world bench in the domain of recommendation in interactive configuration

The complexity of unsupervised learning of lexicographic preferences

International audienceThis paper considers the task of learning users' preferences on a combinatorial set of alternatives, as generally used by online configurators, for example. In many settings, only a set of selected alternatives during past interactions is available to the learner. Fargier et al. [2018] propose an approach to learn, in such a setting, a model of the users' preferences that ranks previously chosen alternatives as high as possible; and an algorithm to learn, in this setting, a particular model of preferences: lexicographic preferences trees (LP-trees). In this paper, we study complexity-theoretical problems related to this approach. We give an upper bound on the sample complexity of learning an LP-tree, which is logarithmic in the number of attributes. We also prove that computing the LP tree that minimises the empirical risk can be done in polynomial time when restricted to the class of linear LP-trees

A theorem prover for default logic based on prioritized conflict resolution and an extended resolution principle

International audienceThis paper presents a theorem prover for Reiter's default logic, one of the most studied nonmonotonic logics. Our theorem prover is based on a decomposition of default logic into two main elements: we describe an extension of the resolution principle, that handles the “monotonic” aspect of the defaults, and we provide a generalization of Reiter's and Levy's algorithms for the computation of hitting sets, that takes care of the nonmonotonic part of default logic. Lastly, we describe how these two components can be separately modified in order to obtain theorem provers for other variants of default logic, notably prioritized default logic