Leading Strategies in Competitive On-Line Prediction

  • Vladimir Vovk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4264)


We start from a simple asymptotic result for the problem of on-line regression with the quadratic loss function: the class of continuous limited-memory prediction strategies admits a “leading prediction strategy”, which not only asymptotically performs at least as well as any continuous limited-memory strategy but also satisfies the property that the excess loss of any continuous limited-memory strategy is determined by how closely it imitates the leading strategy. More specifically, for any class of prediction strategies constituting a reproducing kernel Hilbert space we construct a leading strategy, in the sense that the loss of any prediction strategy whose norm is not too large is determined by how closely it imitates the leading strategy. This result is extended to the loss functions given by Bregman divergences and by strictly proper scoring rules.


Loss Function Reproduce Kernel Hilbert Space Prediction Strategy Predictable Process Quadratic Loss Function 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Vladimir Vovk
    • 1
  1. 1.Computer Learning Research Centre, Department of Computer ScienceUniversity of LondonEgham, SurreyUK

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