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.

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