  We introduce in this paper a new algorithm for Multi-Armed Bandit (MAB)
problems. A machine learning paradigm popular within Cognitive Network related
topics (e.g., Spectrum Sensing and Allocation). We focus on the case where the
rewards are exponentially distributed, which is common when dealing with
Rayleigh fading channels. This strategy, named Multiplicative Upper Confidence
Bound (MUCB), associates a utility index to every available arm, and then
selects the arm with the highest index. For every arm, the associated index is
equal to the product of a multiplicative factor by the sample mean of the
rewards collected by this arm. We show that the MUCB policy has a low
complexity and is order optimal.
