Nawal Benabbou

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.

On Possibly Optimal Tradeoffs in Multicriteria Spanning Tree Problems

In this paper, we propose an interactive approach to determine a compromise solution in the multicriteria spanning tree problem. We assume that the Decision Makers preferences over spanning trees can be represented by a weighted sum of criteria but that weights are imprecisely known. In the first part of the paper, we propose a generalization of Prims algorithm to determine the set of possibly optimal tradeoffs. In the second part, we propose an incremental weight elicitation method to reduce the set of feasible weights so as to identify a necessary optimal tradeoff. Numerical tests are given to demonstrate the practical feasibility of the approach.

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.

Adaptive Elicitation of Preferences under Uncertainty in Sequential Decision Making Problems

This paper aims to introduce an adaptive preference elicitation method for interactive decision support in sequential decision problems. The Decision Makers preferences are assumed to be representable by an additive utility, initially unknown or imperfectly known. We first study the determination of possibly optimal policies when admissible utilities are imprecisely defined by some linear constraints derived from observed preferences. Then, we introduce a new approach interleaving elicitation of utilities and backward induction to incrementally determine a near-optimal policy. We propose an interactive algorithm with performance guarantees and describe numerical tests demonstrating the practical efficiency of our approach.

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.

Incremental Decision Making Under Risk with the Weighted Expected Utility Model

This paper deals with decision making under risk with the Weighted Expected Utility (WEU) model, which is a model generalizing expected utility and providing stronger descriptive possibilities. We address the problem of identifying, within a given set of lotteries, a (near-)optimal solution for a given decision maker consistent with the WEU theory. The WEU model is parameterized by two real-valued functions. We propose here a new incremental elicitation procedure to progressively reduce the imprecision about these functions until a robust decision can be made. We also give experimental results showing the practical efficiency of our method.

Possible Optimality and Preference Elicitation for Decision Making

Decision support systems often rely on a mathematical decision model allowing the comparison of alternatives and the selection of a proper solution.