Review for NeurIPS paper: Temporal Variability in Implicit Online Learning

This paper considers the implicit update algorithm for online learning (a.k.a. It is shown that the algorithm achieves a regret bound that is adapted to the variability of the sequence of loss functions. This holds even without the smoothness of the loss. I believe this is a firm contribution to the fields of online learning and stochastic optimization. Firstly, Implicit updates are known to have practical advantages, but their theoretical understanding has been limited to the fact that they enjoy the same worst-case regret guarantees as their explicit counterparts. This is one of a very few works (if not the first one) which shows a nontrivial advantages of the implicit methods and thus makes a significant progress in better understanding of their behavior.