On Some Optimization Problems for the Rényi Divergence

Аннотация

We consider the problem of determining the maximum and minimum of the Rényi divergence D_λ(P||Q) and D_λ(Q||P) for two probability distribution P and Q of discrete random variables X and Y provided that the probability distribution P and the parameter α of α-coupling between X and Y are fixed, i.e., provided that Pr{X = Y } = α.