Open Problem: Do you pay for Privacy in Online learning?

Online learning, in the mistake bound model, is one of the most fundamental concepts in learning theory and differential privacy is, perhaps, the most widely used statistical concept of privacy in the machine learning community. Thus, defining problems which are online differentially privately learnable is of great interest in learning theory. In this paper, we pose the question on if the two problems are equivalent from a learning perspective, i.e., is privacy for free in the online learning framework?