Learning Lexicographic Preference Models

Abstract

Lexicographic preference models (LPMs) are one of the simplest yet most commonly used preference representations. In this chapter, we formally define LPMs and present learning algorithms for mining these models from data. In particular, we study a greedy algorithm that produces a “best guess” LPM that is consistent with the observations and two voting-based algorithms that approximate the target using the votes of a collection of consistent LPMs. In addition to our theoretical analyses of these algorithms, we empirically evaluate their performance under different conditions. Our results show that voting algorithms outperform the greedy method when the data is noise-free. The dominance is more significant when the training data is scarce. However, the performance of the voting algorithms quickly decays with even a little noise, whereas the greedy algorithm is more robust. Inspired by this result, we adapt one of the voting methods to consider the amount of noise in an environment and empirically show that the modified voting algorithm performs as well as the greedy approach even with noisy observations. We also introduce an intuitive yet powerful learning bias to prune some of the possible LPMs. We demonstrate how this learning bias can be used with variable and model voting and show that the learning bias improves learning performance significantly, especially when the number of observations is small.