On Calibration Error of Randomized Forecasting Algorithms

  • Authors:

  • Vladimir V. V'Yugin

  • Affiliations:

  • Institute for Information Transmission Problems, Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, Moscow GSP-4, 127994, Russia

  • Venue:
  • ALT '07 Proceedings of the 18th international conference on Algorithmic Learning Theory
  • Year:
  • 2007

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Abstract

Recently, it was shown that calibration with an error less than 茂戮驴 0 is almost surely guaranteed with a randomized forecasting algorithm, where forecasts are chosen using randomized rounding up to 茂戮驴of deterministic forecasts. We show that this error can not be improved for a large majority of sequences generated by a probabilistic algorithm: we prove that combining outcomes of coin-tossing and a transducer algorithm, it is possible to effectively generate with probability close to one a sequence "resistant" to any randomized rounding forecasting with an error much smaller than 茂戮驴.