Kurzbeschreibung: Prediction with expert advice" is a rich setting studied under many different variations. It can be described as follows: we want to repeatedly forecast a target quantity of interest, and have the possibility to ask a finite family of "experts", or predictors, about their opinion on the matter (i.e. their own best guess for the next outcome). Then we form our own forecast on the basis of this information, typically by a suitable convex combination of the individual expert predictions. The prediction skills of the individual experts may be very variable and are not known a priori, so that we have to assess their skill from their performance on N past outcomes and decide accordingly how to trust their opinion. A common goal is to keep the regret as low as possible, that is, our average excess prediction error in comparison to the best expert (had they been known in advance). In general a "slow rate" control of the regret is possible, of order 1/sqrt(N). Under certain circumstances (linked to strong convexity of the prediction loss function) a "fast rate" decay of order 1/N can be reached. We will review some key established results then study the possibility of such fast rates under the additional constraint that the number of experts consulted each round is limited, or that there is a limited total "expert query budget". An important finding in a nutshell is that it is necessary and sufficient to be able to consult at least 2 experts per prediction round to be able to reach such fast rates. (This is joint work with El Mehdi Saad.)