Paolo Viappiani

Incremental elicitation of choquet capacities for multicriteria decision making

The Choquet integral is one of the most sophisticated and expressive preference models used in decision theory for multicriteria decision making. It performs a weighted aggregation of criterion values using a capacity function assigning a weight to any coalition of criteria, thus enabling positive and/or negative interactions among criteria and covering an important range of possible decision behaviors. However, the specification of the capacity involves many parameters which raises challenging questions, both in terms of elicitation burden and guarantee on the quality of the final recommendation. In this paper, we investigate the incremental elicitation of the capacity through a sequence of preference queries selected one-by-one using a minimax regret strategy so as to progressively reduce the set of possible capacities until a decision can be made. We propose a new approach designed to efficiently compute minimax regret for the Choquet model. Numerical experiments are provided to demonstrate the practical efficiency of our approach.

Preferences in artificial intelligence

The paper presents a focused survey about the presence and the use of the concept of “preferences” in Artificial Intelligence. Preferences are a central concept for decision making and have extensively been studied in disciplines such as economy, operational research, decision analysis, psychology and philosophy. However, in the recent years it has also become an important topic both for research and applications in Computer Science and more specifically in Artificial Intelligence, in fields spanning from recommender systems to automatic planning, from non monotonic reasoning to computational social choice and algorithmic decision theory. The survey essentially covers the basics of preference modelling, the use of preference in reasoning and argumentation, the problem of compact representations of preferences, preference learning and the use of non conventional preference models based on extended logical languages. It aims at providing a general reference for all researchers both in Artificial Intelligence and Decision Analysis interested in this exciting interdisciplinary topic.

Reducing the Number of Queries in Interactive Value Iteration

To tackle the potentially hard task of defining the reward function in a Markov Decision Process MDPs, a new approach, called Interactive Value Iteration IVI has recently been proposed by Weng and Zanuttini 2013. This solving method, which interweaves elicitation and optimization phases, computes a near optimal policy without knowing the precise reward values. The procedure as originally presented can be improved in order to reduce the number of queries needed to determine an optimal policy. The key insights are that 1 asking queries should be delayed as much as possible, avoiding asking queries that might not be necessary to determine the best policy, 2 queries should be asked by following a priority order because the answers to some queries can enable to resolve some other queries, 3 queries can be avoided by using heuristic information to guide the process. Following these ideas, a modified IVI algorithm is presented and experimental results show a significant decrease in the number of queries issued.

Incremental elicitation of Choquet capacities for multicriteria choice, ranking and sorting problems

This paper proposes incremental preference elicitation methods for multicriteria decision making with a Choquet integral. The Choquet integral is an evaluation function that performs a weighted aggregation of criterion values using a capacity function assigning a weight to any coalition of criteria, thus enabling positive and/or negative interactions among them and covering an important range of possible decision behaviors. However, the specification of the capacity involves many parameters which raises challenging questions, both in terms of elicitation burden and guarantee on the quality of the final recommendation.In this paper, we investigate the incremental elicitation of the capacity through a sequence of preference queries (questions) selected one-by-one using a minimax regret strategy so as to progressively reduce the set of possible capacities until the regret (the worst-case loss due to reasoning with only partially specified capacities) is low enough. We propose a new approach designed to efficiently compute minimax regret for the Choquet model and we show how this approach can be used in different settings: 1) the problem of recommending a single alternative, 2) the problem of ranking alternatives from best to worst, and 3) sorting several alternatives into ordered categories. Numerical experiments are provided to demonstrate the practical efficiency of our approach for each of these situations.

Incremental Preference Elicitation in Multi-attribute Domains for Choice and Ranking with the Borda Count

In this paper, we propose an interactive version of the Borda method for collective decision-making (social choice) when the alternatives are described with respect to multiple attributes and the individual preferences are unknown. More precisely, assuming that individual preferences are representable by linear multi-attribute utility functions, we propose an incremental elicitation method aiming to determine the Borda winner while minimizing the communication effort with the agents. This approach follows the recent work of Lu and Boutilier [8] relying on the minimax regret as a criterion for dealing with uncertainty in the preferences. We show that, when preferences are expressed on a multi-attribute domain and are additively separable over attributes, regret-based incremental elicitation methods can be made more efficient to determine or approximate the Borda winner. Our approach relies on the representation of incomplete preferences using convex polyhedra of possible utilities and is based on linear programming both for minimizing regrets and selecting informative preference queries. It enables to incrementally collect preference judgements from the agents until the Borda winner can be identified. Moreover, we provide an incremental technique for eliciting a collective ranking instead of a single winner.

Constructive Preference Elicitation for Multiple Users with Setwise Max-margin

In this paper we consider the problem of simultaneously eliciting the preferences of a group of users in an interactive way. We focus on constructive recommendation tasks, where the instance to be recommended should be synthesized by searching in a constrained configuration space rather than choosing among a set of pre-determined options. We adopt a setwise max-margin optimization method, that can be viewed as a generalization of max-margin learning to sets, supporting the identification of informative questions and encouraging sparsity in the parameter space. We extend setwise max-margin to multiple users and we provide strategies for choosing the user to be queried next and identifying an informative query to ask. At each stage of the interaction, each user is associated with a set of parameter weights (a sort of alternative options for the unknown user utility) that can be used to identify “similar” users and to propagate preference information between them. We present simulation results evaluating the effectiveness of our procedure, showing that our approach compares favorably with respect to straightforward adaptations in a multi-user setting of elicitation methods conceived for single users.

Aggregation of Uncertain Qualitative Preferences for a Group of Agents

We consider aggregation of partially known qualitative preferences for a group of agents, considering necessary and potentially optimal choices with respect to different notions of optimality (consensus, extreme choices, Pareto optimality) and provide a theoretical characterization. We report statistics (obtained with simulations with synthetic data) about the cardinality of the sets of possible and necessarily optimal choices for the different cases. Finally we introduce preliminary ideas on a qualitative notion of fairness and on interactive elicitation.