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Tracking the Optimal Sequence of Predictive Strategies

  • V. V. V’yuginEmail author
  • V. G. TrunovEmail author
THEORY AND METHODS OF INFORMATION PROCESSING
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Abstract

Within the prediction (decision making) theory with online experts, an adaptive algorithm is proposed that aggregates the decisions of expert strategies and incurs losses that do not exceed (up to a certain value, called a regret) the losses of the best combination of experts distributed over the prediction interval. The algorithm develops the Mixing Past Posteriors method and the AdaHedge algorithm of exponential weighting of expert decisions using an adaptive learning parameter. An estimate of the regret of the proposed algorithm is obtained. The approach proposed does not make assumptions about the nature of the data source and the limits of experts’ losses. The results of numerical experiments on mixing expert solutions using the proposed algorithm under conditions of high volatility of experts’ losses are given.

Keywords:

online loss distribution algorithms predictions using expert strategies mixing schemes for posterior expert distributions adaptive learning parameter 

Notes

ACKNOWLEDGMENTS

This work was supported by the Russian Science Foundation, project no. 14-50-00150.

REFERENCES

  1. 1.
    V. V’yugin, “Online aggregation of unbounded signed losses using shifting experts,” in Proc. Mach. Learn. Res. 60, 3–17 (2017). http://proceedings.mlr. press/v60/v-yugin17a.html.Google Scholar
  2. 2.
    N. Littlestone and M. Warmuth, “The weighted majority algorithm,” Inform. Comput. 108, 212–261 (1994).Google Scholar
  3. 3.
    Y. Freund and R. E. Schapire, “A decision-theoretic generalization of on-line learning and an application to boosting,” J. Comput. Syst. Sci. 55, 119–139 (1997).Google Scholar
  4. 4.
    V. Vovk, “Aggregating Strategies,” in Proc. 3rd Ann. Workshop on Computational Learning Theory, San Mateo, CA, 1990, Ed. by M. Fulk and J. Case (Morgan Kaufmann, 1990), pp. 371–383.Google Scholar
  5. 5.
    V. Vovk, “A game of prediction with expert advice,” J. Comput. Syst. Sci. Elsevier Publ. 56 (2), 153–173 (1998).Google Scholar
  6. 6.
    N. Cesa-Bianchi and G. Lugosi, Prediction, Learning, and Games (Cambridge Univ. Press, Cambridge, 2006).CrossRefzbMATHGoogle Scholar
  7. 7.
    V. V. V’yugin, Mathematical Foundation of Machine Learning and Forecasting (MTsN-MO, Moscow, 2018) [in Russian].Google Scholar
  8. 8.
    S. de Rooij, T. van Erven, P. Grunwald, and W. Koolen, “Follow the leader if you can, hedge if you must,” J. Mach. Learn. Res. 15, 1281–1316 (2004).Google Scholar
  9. 9.
    M. Herbster and M. Warmuth, “Tracking the best expert,” Machine Learning (Springer) 32 (2), 151–178 (1998).Google Scholar
  10. 10.
    O. Bousquet and M. Warmuth, “Tracking a small set of experts by mixing past posteriors,” J. Mach. Learn. Res, No. 3, 363–396 (2002).zbMATHGoogle Scholar
  11. 11.
    V. V. V’yugin, I. A. Stel’makh, and V. G. Trunov, “Adaptive algorithm of tracking the best experts trajectory,” J. Commun. Technol. Electron. 62, 1434–1447 (2017).Google Scholar
  12. 12.
    V. V. V’yugin and V. G. Trunov, “Applications of combined financial strategies based on universal adaptive forecasting,” Autom. Remote Control. 77, 1428–1446 (2016).Google Scholar
  13. 13.
    V. V. V’yugin, “Universal algorithm for trading in stock market based on the method of calibration,” in Algorithmic Learning Theory (ALT 2013). Lect. Notes in Computer Science, Ed. by S. Jain, R. Munos, F. Stephan, and T. Zeugmann (Springer-Verlag, Berlin, 2013), Vol. 8139.Google Scholar
  14. 14.
    V. Vovk, “Derandomizing stochastic prediction strategies,” Machine Learning 35, 247–282 (1999).Google Scholar
  15. 15.
    J. Kivinen and M. K. Warmuth, “Averaging expert prediction,” in Proc. 4th Eur. Conf. (EuroColt ’99) on Computational Learning Theory, 1999, Ed. by P. Fisher and H. U. Simon (Springer-Verlag, 1999), pp. 153–167.Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Kharkevich Institute for Information Transmission Problems, Russian Academy of SciencesMoscowRussia

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