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In this paper the sequential prediction problem with expert advice isconsidered for the case where losses of experts suffered at each step cannot bebounded in advance. We present some modification of Kalai and Vempala algorithmof following the perturbed leader where weights depend on past losses of theexperts. New notions of a volume and a scaled fluctuation of a game areintroduced. We present a probabilistic algorithm protected from unrestrictedlylarge one-step losses. This algorithm has the optimal performance in the casewhen the scaled fluctuations of one-step losses of experts of the pool tend tozero.

Online Learning in Case of Unbounded Losses Using the Follow Perturbed Leader Algorithm