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Learning Foraging Thresholds for Lizards

This work gives a proof of convergence for a randomized learning algorithm that describes how anoles (lizards found in the Carribean) learn a foraging threshold distance. The model assumes that an anole will pursue a prey if and only if it is within this threshold of the anole''s perch. This learning algorithm was proposed by the biologist Roughgarden and his colleagues. They experimentally confirmed that this algorithm quickly converges to the foraging threshold that is predicted by optimal foraging theory. Our analysis provides an analytic confirmation that the learning algorithm converges to this optimal foraging threshold with high probability.