We consider learning problems of an intuitive and concise preference model, called lexicographic preference lists (LP-lists). Given a set of examples that are pairwise ordinal preferences over a universe of objects built of attributes of discrete values, we want to learn (1) an optimal LP-list that decides the maximum number of these examples, or (2) a near-optimal LP-list that decides as many examples as it can. To this end, we introduce a dynamic programming based algorithm and a genetic algorithm for these two learning problems, respectively. Furthermore, we empirically demonstrate that the sub-optimal models computed by the genetic algorithm very well approximate the de facto optimal models computed by our dynamic programming based algorithm, and that the genetic algorithm outperforms the baseline greedy heuristic with higher accuracy predicting new preferences.
Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences, most notably lexicographic ones. The proposed logic supports a simple new connective whose semantics can be defined in terms of finite lists of truth values. We demonstrate that, despite the well-known theoretical limitations that pose barriers to the quantitative representation of lexicographic preferences, there exists a subset of the rational numbers over …
This 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-theoretic…
In most common settings of Markov Decision Process (MDP), an agent evaluate a policy based on expectation of (discounted) sum of rewards. However in many applications this criterion might not be suitable from two perspective: first, in risk aversion situation expectation of accumulated rewards is not robust enough, this is the case when distribution of accumulated reward is heavily skewed; another issue is that many applications naturally take several objective into consideration when evaluating a policy, for instance in autonomous driving an agent needs to balance speed and safety when choosi…
DISIT - Università del Piemonte Orientale（皮埃蒙特东方大学）
We define a modular multi-concept extension of the lexicographic closure semantics for defeasible description logics with typicality. The idea is that of distributing the defeasible properties of concepts into different modules, according to their subject, and of defining a notion of preference for each module based on the lexicographic closure semantics. The preferential semantics of the knowledge base can then be defined as a combination of the preferences of the single modules. The range of possibilities, from fine grained to coarse grained modules, provides a spectrum of alternative semant…
In this work, we present a novel human-in-the-loop framework to help the human user understand the decision making process that involves choosing preferred options. We focus on qualitative preference models over alternatives from combinatorial domains. This framework is interactive: the user provides her behavioral data to the framework, and the framework explains the learned model to the user. It is iterative: the framework collects feedback on the learned model from the user and tries to improve it accordingly till the user terminates the iteration. In order to communicate the learned prefer…
Lexicographic optimization-based approaches to learning a representative model for multi-criteria sorting with non-monotonic criteria
School of Economics and Management, Dalian University of Technology（大连理工大学经济管理学院）；School of Data Science and Artificial Intelligence, Dongbei University of Finance and Economics（东北财经大学数据科学与人工智能学院）
Selecting a set of alternatives based on the preferences of agents is an important problem in committee selection and beyond. Among the various criteria put forth for the desirability of a committee, Pareto optimality is a minimal and important requirement. As asking agents to specify their preferences over exponentially many subsets of alternatives is practically infeasible, we assume that each agent specifies a weak order on single alternatives, from which a preference relation over subsets is derived using some preference extension. We consider five prominent extensions (responsive, downwar…
Peking University（北京大学）；Washington University in St. Louis（圣路易斯华盛顿大学）；Rensselaer Polytechnic Institute（伦斯勒理工学院）
In multi-type resource allocation (MTRA) problems, there are p $\ge$ 2 types of items, and n agents, who each demand one unit of items of each type, and have strict linear preferences over bundles consisting of one item of each type. For MTRAs with indivisible items, our first result is an impossibility theorem that is in direct contrast to the single type (p = 1) setting: No mechanism, the output of which is always decomposable into a probability distribution over discrete assignments (where no item is split between agents), can satisfy both sd-efficiency and sd-envy-freeness. To circumvent t…
University of Regina（里贾纳大学）；Department of Computer Science（计算机科学系）
The Conditional Preference Network (CP-net) graphically represents user's qualitative and conditional preference statements under the ceteris paribus interpretation. The constrained CP-net is an extension of the CP-net, to a set of constraints. The existing algorithms for solving the constrained CP-net require the expensive dominance testing operation. We propose three approaches to tackle this challenge. In our first solution, we alter the constrained CP-net by eliciting additional relative importance statements between variables, in order to have a total order over the outcomes. We call this…
The stable marriage problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. We consider a useful variation of the stable marriage problem, where the men and women express their preferences using a preference list with ties over a subset of the members of the other sex. Matchings are permitted only with people who appear in these preference lists. In this setting, we study the problem of finding a stable matching that marries as many people as possible. Stability is an …
We present our experimental results of simulating the school choice problem which deals with the assignment of students to schools based on each group's complete preference list for the other group using two algorithms: Boston mechanism and student-proposing Gale-Shapley algorithm. We compare the effects of sophisticated students altering their preference lists with regards to these two algorithms. Our simulation results show that sophisticated students can benefit more in Boston mechanism compared to Gale-Shapley algorithm based on multiple evaluation metrics.
