  We specify an experts algorithm with the following characteristics: (a) it
uses only feedback from the actions actually chosen (bandit setup), (b) it can
be applied with countably infinite expert classes, and (c) it copes with losses
that may grow in time appropriately slowly. We prove loss bounds against an
adaptive adversary. From this, we obtain master algorithms for "active experts
problems", which means that the master's actions may influence the behavior of
the adversary. Our algorithm can significantly outperform standard experts
algorithms on such problems. Finally, we combine it with a universal expert
class. This results in a (computationally infeasible) universal master
algorithm which performs - in a certain sense - almost as well as any
computable strategy, for any online problem.
