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Minimizing Regret with Label Efficient Prediction

  • Nicolò Cesa-Bianchi
  • Gábor Lugosi
  • Gilles Stoltz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3120)

Abstract

We investigate label efficient prediction, a variant of the problem of prediction with expert advice, proposed by Helmbold and Panizza, in which the forecaster does not have access to the outcomes of the sequence to be predicted unless he asks for it, which he can do for a limited number of times. We determine matching upper and lower bounds for the best possible excess error when the number of allowed queries is a constant. We also prove that a query rate of order (ln n) (ln ln n)2/n is sufficient for achieving Hannan consistency, a fundamental property in game-theoretic prediction models. Finally, we apply the label efficient framework to pattern classification and prove a label efficient mistake bound for a randomized variant of Littlestone’s zero-threshold Winnow algorithm.

Keywords

Loss Function Expert Advice Repeated Game Query Rate Cumulative Loss 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Auer, P., Cesa-Bianchi, N., Freund, Y., Schapire, R.E.: The nonstochastic multiarmed bandit problem. SIAM Journal on Computing 32(1), 48–77 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Auer, P., Cesa-Bianchi, N., Gentile, C.: Adaptive and self-confident on-line learning algorithms. Journal of Computer and System Sciences 64(1) (2002)Google Scholar
  3. 3.
    Birgé, L.: A new look at an old result: Fano’s lemma. Technical report, Université Paris 6 (2001) Google Scholar
  4. 4.
    Cesa-Bianchi, N., Freund, Y., Haussler, D., Helmbold, D.P., Schapire, R., Warmuth, M.K.: How to use expert advice. Journal of the ACM 44(3), 427–485 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Chow, Y.S., Teicher, H.: Probability Theory. Springer, Heidelberg (1988)zbMATHGoogle Scholar
  6. 6.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory. John Wiley and Sons, Chichester (1991)zbMATHCrossRefGoogle Scholar
  7. 7.
    Hannan, J.: Approximation to Bayes risk in repeated play. Contributions to the theory of games 3, 97–139 (1957)Google Scholar
  8. 8.
    Helmbold, D.P., Panizza, S.: Some label efficient learning results. In: Proceedings of the 10th Annual Conference on Computational Learning Theory, pp. 218–230. ACM Press, New York (1997)CrossRefGoogle Scholar
  9. 9.
    Hoeffding, W.: Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58, 13–30 (1963)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Littlestone, N.: Mistake Bounds and Logarithmic Linear-threshold Learning Algorithms. PhD thesis, University of California at Santa Cruz (1989) Google Scholar
  11. 11.
    Massart, P.: Concentration inequalities and model selection. Saint-Flour summer school lecture notes (2003) (to appear) Google Scholar
  12. 12.
    Piccolboni, A., Schindelhauer, C.: Discrete prediction games with arbitrary feedback and loss. In: Proceedings of the 14th Annual Conference on Computational Learning Theory, pp. 208–223 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Nicolò Cesa-Bianchi
    • 1
  • Gábor Lugosi
    • 2
  • Gilles Stoltz
    • 3
  1. 1.DSIUniversità di MilanoMilanoItaly
  2. 2.Department of EconomicsUniversitat Pompeu FabraBarcelonaSpain
  3. 3.Laboratoire de MathématiquesUniversité Paris-SudOrsay CedexFrance

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