  Optimistic Online Learning algorithms have been developed to exploit expert
advices, assumed optimistically to be always useful. However, it is legitimate
to question the relevance of such advices \emph{w.r.t.} the learning
information provided by gradient-based online algorithms. In this work, we
challenge the confidence assumption on the expert and develop the
\emph{optimistically tempered} (OT) online learning framework as well as OT
adaptations of online algorithms. Our algorithms come with sound theoretical
guarantees in the form of dynamic regret bounds, and we eventually provide
experimental validation of the usefulness of the OT approach.
