A Closer Look at Adaptive Regret

  • Dmitry Adamskiy
  • Wouter M. Koolen
  • Alexey Chernov
  • Vladimir Vovk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7568)


For the prediction with expert advice setting, we consider methods to construct algorithms that have low adaptive regret. The adaptive regret of an algorithm on a time interval [t 1,t 2] is the loss of the algorithm there minus the loss of the best expert. Adaptive regret measures how well the algorithm approximates the best expert locally, and it is therefore somewhere between the classical regret (measured on all outcomes) and the tracking regret, where the algorithm is compared to a good sequence of experts.

We investigate two existing intuitive methods to derive algorithms with low adaptive regret, one based on specialist experts and the other based on restarts. Quite surprisingly, we show that both methods lead to the same algorithm, namely Fixed Share, which is known for its tracking regret. Our main result is a thorough analysis of the adaptive regret of Fixed Share. We obtain the exact worst-case adaptive regret for Fixed Share, from which the classical tracking bounds can be derived. We also prove that Fixed Share is optimal, in the sense that no algorithm can have a better adaptive regret bound.


Online learning adaptive regret Fixed Share specialist experts 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Dmitry Adamskiy
    • 1
  • Wouter M. Koolen
    • 1
  • Alexey Chernov
    • 2
  • Vladimir Vovk
    • 1
  1. 1.Computer Learning Research Centre and Department of Computer ScienceRoyal Holloway, University of LondonSurreyUK
  2. 2.Department Mathematical SciencesDurham UniversityDurhamUK

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