Reviews: Parameter-Free Online Learning via Model Selection

SUMMARY While I am not heavily familiar with the literature on adaptive online learning, this paper seems to be a breakthrough, offering in the form of Theorem 1 a very strong result that can be leveraged to obtain adaptive (in the model complexity sense) online learning bounds in a number of settings. The efficiency, at least in the polytime sense, of the algorithms for the various settings makes these results all the more interesting. I was very surprised by the aside'' on the 1-mixability of logistic loss and the argument for circumventing the lower bound of Hazan, Koren, and Levy in the supervised learning setting. I wish that the authors could give more detail to this observation and the consequences, as the implications are so interesting that I would be (almost) sold on acceptance from this fact alone. I found the results of this paper to be very interesting, technically strong, and important, so I would strongly recommend acceptance.