Learning Optimal and Near-Optimal Lexicographic Preference Lists

TL;DR

This paper introduces algorithms for learning lexicographic preference lists from pairwise preferences, focusing on optimizing the number of correctly decided examples, and demonstrates their effectiveness through empirical evaluation.

Contribution

It presents a dynamic programming algorithm for optimal learning and a genetic algorithm for near-optimal learning of LP-lists, with empirical validation.

Findings

Genetic algorithm closely approximates optimal models.

Genetic algorithm outperforms baseline heuristics.

Empirical results show high accuracy in preference prediction.

Abstract

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.