A Theory of Optimistically Universal Online Learnability for General Concept Classes

We provide a full characterization of the concept classes that are optimistically universally online learnable with {0, 1} labels. The notion of optimistically universal online learning was defined in [Hanneke, 2021] in order to understand learnability under minimal assumptions. In this paper, following the philosophy behind that work, we investigate two questions, namely, for every concept class: (1) What are the minimal assumptions on the data process admitting online learnability?