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Prediction with Expert Advice under Discounted Loss

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6331))

Abstract

We study prediction with expert advice in the setting where the losses are accumulated with some discounting and the impact of old losses can gradually vanish. We generalize the Aggregating Algorithm and the Aggregating Algorithm for Regression, propose a new variant of exponentially weighted average algorithm, and prove bounds on the cumulative discounted loss.

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References

  1. Beckenbach, E.F., Bellman, R.: Inequalities. Springer, Berlin (1961)

    Google Scholar 

  2. Cesa-Bianchi, N., Lugosi, G.: Prediction, learning, and games. Cambridge University Press, Cambridge (2006)

    Book  MATH  Google Scholar 

  3. Chaudhuri, K., Freund, Y., Hsu, D.: A parameter-free hedging algorithm. In: Advances in Neural Information Processing Systems, vol. 22, pp. 297–305 (2009)

    Google Scholar 

  4. Chernov, A., Kalnishkan, Y., Zhdanov, F., Vovk, V.: Supermartingales in prediction with expert advice. Theoretical Computer Science 411, 2647–2669 (2010); See also: arXiv:1003.2218 [cs.LG]

    Article  MATH  MathSciNet  Google Scholar 

  5. Chernov, A., Vovk, V.: Prediction with advice of unknown number of experts. In: Proc. of 26th Conf. on Uncertainty in Artificial Intelligence, pp. 117–125 (2010)

    Google Scholar 

  6. Chernov, A., Zhdanov, F.: Prediction with expert advice under discounted loss. Technical report, arXiv:1005.1918v1 [cs.LG] (2010)

    Google Scholar 

  7. Freund, Y., Hsu, D.: A new hedging algorithm and its application to inferring latent random variables. Technical report, arXiv:0806.4802v1 [cs.GT] (2008)

    Google Scholar 

  8. Gammerman, A., Kalnishkan, Y., Vovk, V.: On-line prediction with kernels and the complexity approximation principle. In: Proc. of 20th Conf. on Uncertainty in Artificial Intelligence, pp. 170–176 (2004)

    Google Scholar 

  9. Gardner, E.S.: Exponential smoothing: The state of the art – part II. International Journal of Forecasting 22, 637–666 (2006)

    Article  Google Scholar 

  10. Harville, D.A.: Matrix algebra from a statistician’s perspective. Springer, Heidelberg (1997)

    MATH  Google Scholar 

  11. Haussler, D., Kivinen, J., Warmuth, M.: Sequential prediction of individual sequences under general loss functions. IEEE Transactions on Information Theory 44, 1906–1925 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  12. Herbster, M., Warmuth, M.K.: Tracking the best expert. Machine Learning 32, 151–178 (1998)

    Article  MATH  Google Scholar 

  13. Kalnishkan, Y., Vyugin, M.: The weak aggregating algorithm and weak mixability. Technical report, CLRC-TR-03-01 (2003)

    Google Scholar 

  14. Kalnishkan, Y., Vyugin, M.: The weak aggregating algorithm and weak mixability. Journal of Computer and System Sciences 74(8), 1228–1244 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  15. Muth, J.F.: Optimal properties of exponentially weighted forecasts. Journal of the American Statistical Association 55, 299–306 (1960)

    Article  MATH  Google Scholar 

  16. Schölkopf, B., Smola, A.J.: Learning with kernels: Support Vector Machines, regularization, optimization, and beyond. MIT Press, Cambridge (2002)

    Google Scholar 

  17. Sutton, R., Barto, A.: Reinforcement learning: An introduction. MIT Press, Cambridge (1998)

    Google Scholar 

  18. Vovk, V.: Aggregating strategies. In: Proc. of 3rd COLT, pp. 371–383 (1990)

    Google Scholar 

  19. Vovk, V.: A game of prediction with expert advice. Journal of Computer and System Sciences 56, 153–173 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  20. Vovk, V.: Derandomizing stochastic prediction strategies. Machine Learning 35, 247–282 (1999)

    Article  MATH  Google Scholar 

  21. Vovk, V.: Competitive on-line statistics. Int. Stat. Review 69, 213–248 (2001)

    MATH  Google Scholar 

  22. Vovk, V.: On-line regression competitive with reproducing kernel Hilbert spaces. Technical report, arXiv:cs/0511058 [cs.LG] (2005)

    Google Scholar 

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Chernov, A., Zhdanov, F. (2010). Prediction with Expert Advice under Discounted Loss. In: Hutter, M., Stephan, F., Vovk, V., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 2010. Lecture Notes in Computer Science(), vol 6331. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16108-7_22

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  • DOI: https://doi.org/10.1007/978-3-642-16108-7_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16107-0

  • Online ISBN: 978-3-642-16108-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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