Playing the matching-shoulders lob-pass game with logarithmic regret

ABSTRACT

The best previous algorithm for the matching shoulders lob-pass game, ARTHUR (Abe and Takeuchi 1993), suffered O(t^1/2) 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.

References

1. Abe, N. and Takeuchi, J. (1993). The lob-pass problem and an on-line learning model of rational choice. In Workshop on Computatwnal Learning Theory, pp. 422-428.
2. Borgstrom, R. S. and Kosaraju, S. R. (1993). Comp~rieon-B~sed Search in the Pre~ence of Errors. In Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, pp. 130-136.
3. Herrnstein, R. (1990). Rational Choice Theory. Amerzcan Psychologist, ~5(3), 356-367.
4. Rivest, R., Meyer, A., Kleitman, D., Winklmann, K., and Spencer, J. (1980). Coping with errors in binary search procedures. Journal of Computer and System Sciences, 33, 85-94.

Index Terms

• Computing methodologies

  • Machine learning

• Theory of computation

  • Computational complexity and cryptography

    • Complexity classes

  • Models of computation