Renyi divergence is related to Renyi entropy much like information divergence (also called Kullback-Leibler divergence or relative entropy) is related to Shannon's entropy, and comes up in many settings. It was introduced by Renyi as a measure of information that satisfies almost the same axioms as information divergence. We review the most important properties of Renyi divergence, including its relation to some other distances. We show how Renyi divergence appears when the theory of majorization is generalized from the finite to the continuous setting. Finally, Renyi divergence plays a role in analyzing the number of binary questions required to guess the values of a sequence of random variables.
['Tim van Erven', 'Peter Harremoës']
Rényi divergence and majorization