Learning Optimal and Near-Optimal Lexicographic Preference Lists

We consider learning problems of an intuitive and concise preference model, called lexicographic preference lists (LP-lists). Given a set of examples that are pair- wise 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 existing greedy heuristic with higher accuracy predicting new preferences.