On learnability of distribution classes with adaptive adversaries

We consider the question of learnability of distribution classes in the presence of adaptive adversaries – that is, adversaries capable of inspecting the whole sample requested by a learner and applying their manipulations before passing it on to the learner. We formulate a general notion of learnability with respect to adaptive adversaries, taking into account the budget of the adversary. We show that learnability with respect to additive adaptive adversaries is a strictly stronger condition than learnability with respect to additive oblivious adversaries.