Chapter

Algorithmic Learning Theory

Volume 5809 of the series Lecture Notes in Computer Science pp 38-52

The Follow Perturbed Leader Algorithm Protected from Unbounded One-Step Losses

  • Vladimir V. V’yuginAffiliated withInstitute for Information Transmission Problems, Russian Academy of Sciences

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Abstract

In this paper the sequential prediction problem with expert advice is considered for the case when the losses of experts suffered at each step can be unbounded. We present some modification of Kalai and Vempala algorithm of following the perturbed leader where weights depend on past losses of the experts. New notions of a volume and a scaled fluctuation of a game are introduced. We present an algorithm protected from unrestrictedly large one-step losses. This algorithm has the optimal performance in the case when the scaled fluctuations of one-step losses of experts of the pool tend to zero.