Abstract
We study preference representation models based on partial lexicographic preference trees (PLP-trees). We propose to represent preference relations as forests of small PLP-trees (PLP-forests), and to use voting rules to aggregate orders represented by the individual trees into a single order to be taken as a model of the agent’s preference relation. We show that when learned from examples, PLP-forests have better accuracy than single PLP-trees. We also show that the choice of a voting rule does not have a major effect on the aggregated order, thus rendering the problem of selecting the “right” rule less critical. Next, for the proposed PLP-forest preference models, we develop methods to compute optimal and near-optimal outcomes, the tasks that appear difficult for some other common preference models. Lastly, we compare our models with those based on decision trees, which brings up questions for future research.
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Notes
- 1.
One can also learn random forests of decision trees. In our experiments, decision trees show high accuracy and seem robust to overfitting. Thus, we do not discuss here results we obtained for random forests.
- 2.
While the preference models we consider here represent total preorders, arguably the most important class of preference relations, we note that some studies of preference relations allow for incomparability of outcomes, which leads to preference relations models by arbitrary preorders (not necessarily total).
- 3.
This captures the idea that the all outcomes in the top cluster in T have their score (with respect to T) equal to the average of \(n-1,n-2,\ldots , n-i\) (with i being the number of outcomes in the top cluster), the outcomes in the next to top cluster have their scores equal to the average of \(n-i-1,n-i-2,\ldots , n-i-j\) (with j being the number of elements in that cluster), etc.
- 4.
The datasets are available at https://www.unf.edu/~N01237497/preflearnlib.php.
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The work of the second author was supported by the NSF grant IIS-1618783.
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Liu, X., Truszczynski, M. (2018). Preference Learning and Optimization for Partial Lexicographic Preference Forests over Combinatorial Domains. In: Ferrarotti, F., Woltran, S. (eds) Foundations of Information and Knowledge Systems. FoIKS 2018. Lecture Notes in Computer Science(), vol 10833. Springer, Cham. https://doi.org/10.1007/978-3-319-90050-6_16
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