# Online nonparametric regression with adversarial data

In this talk, I will consider the problem of online nonparametric regression with arbitrary deterministic sequences. Using ideas from the chaining technique, I will design an algorithm that achieves a Dudley-type regret bound similar to the one obtained in a non-constructive fashion by Rakhlin and Sridharan (2014). The regret bound is expressed in terms of the metric entropy in the sup norm, which yields optimal guarantees when the metric and sequential entropies are of the same order of magnitude. In particular the algorithm is the first one that achieves optimal rates for online regression over Hölder balls.