Randomness criteria in terms of f-divergences

Vovk's randomness criterion characterizes sequences that are random relative to two distinct computable probability measures. The uniqueness of the criterion lies in the fact that, unlike the standard criterion based on the likelihood ratio test, it is expressed in terms of a geometrical quantity, the Hellinger distance, on the space of probability measures. In this talk, I generalize the randomness criteria to a wider class of geometrical quantities, the alpha-divergences with -1<alpha<1. I also mention the possibility of further generalizing the criteria in terms of f-divergences.