Simplicity and Robustness of Fast and Frugal Heuristics
Minds and Machines
Democratic approximation of lexicographic preference models
Proceedings of the 25th international conference on Machine learning
The complexity of learning separable ceteris paribus preferences
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Learning conditionally lexicographic preference relations
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Democratic approximation of lexicographic preference models
Artificial Intelligence
Aggregating conditionally lexicographic preferences on multi-issue domains
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Learning conditional preference network from noisy samples using hypothesis testing
Knowledge-Based Systems
Editorial: Preference learning and ranking
Machine Learning
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Fast and frugal heuristics are well studied models of bounded rationality. Psychological research has proposed the take-the-best heuristic as a successful strategy in decision making with limited resources. Take-the-best searches for a sufficiently good ordering of cues (or features) in a task where objects are to be compared lexicographically. We investigate the computational complexity of finding optimal cue permutations for lexicographic strategies and prove that the problem is NP-complete. It follows that no efficient (that is, polynomial-time) algorithm computes optimal solutions, unless P=NP. We further analyze the complexity of approximating optimal cue permutations for lexicographic strategies. We show that there is no efficient algorithm that approximates the optimum to within any constant factor, unless P=NP. The results have implications for the complexity of learning lexicographic strategies from examples. They show that learning them in polynomial time within the model of agnostic probably approximately correct (PAC) learning is impossible, unless RP=NP. We further consider greedy approaches for building lexicographic strategies and determine upper and lower bounds for the performance ratio of simple algorithms. Moreover, we present a greedy algorithm that performs provably better than take-the-best. Tight bounds on the sample complexity for learning lexicographic strategies are also given in this article.