On the Complexity of Learning Lexicographic Strategies

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. Takethe-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...

• Type: Journal
• Year: 2006
• Where: JMLR
• Authors: Michael Schmitt, Laura Martignon
• Keywords: Algorithm, JMLR 2006, Lexicographic Strategies, Optimal Cue Permutations