  We propose a version of the follow-the-perturbed-leader online prediction
algorithm in which the cumulative losses are perturbed by independent symmetric
random walks. The forecaster is shown to achieve an expected regret of the
optimal order O(sqrt(n log N)) where n is the time horizon and N is the number
of experts. More importantly, it is shown that the forecaster changes its
prediction at most O(sqrt(n log N)) times, in expectation. We also extend the
analysis to online combinatorial optimization and show that even in this more
general setting, the forecaster rarely switches between experts while having a
regret of near-optimal order.
