Comparison-based search in the presence of errors
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
The “lob-pass” problem and an on-line learning model of rational choice
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
A competitive approach to game learning
COLT '96 Proceedings of the ninth annual conference on Computational learning theory
A Computational Role for Dopamine Delivery in Human Decision-Making
Journal of Cognitive Neuroscience
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The best previous algorithm for the matching shoulders lob-pass game, ARTHUR (Abe and Takeuchi 1993), suffered O(t1/2) regret. We prove that this is the best possible performance for any algorithm that works by accurately estimating the opponent's payoff lines. Then we describe an algorithm which beats that bound and meets the information-theoretic lower bound of O(logt) regret by converging to the best lob rate without accurately estimating the payoff lines. The noise-tolerant binary search procedure that we develop is of independent interest.