  In this paper the sequential prediction problem with expert advice is
considered for the case where losses of experts suffered at each step cannot be
bounded in advance. 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 a probabilistic 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.
