  We consider the problem of online nonparametric regression with arbitrary
deterministic sequences. Using ideas from the chaining technique, we 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). Our 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 our algorithm is the first one that achieves
optimal rates for online regression over H{\"o}lder balls. In addition we show
for this example how to adapt our chaining algorithm to get a reasonable
computational efficiency with similar regret guarantees (up to a log factor).
