Online allocation with risk information

We consider the problem of dynamically apportioning resources among a set of options in a worst-case online framework. The model we investigate is a generalization of the well studied online learning model. In particular, we allow the learner to see as additional information how high the risk of each option is. This assumption is natural in many applications like horse-race betting, where gamblers know odds for all options before placing bets. We apply Vovk's Aggregating Algorithm to this problem and give a tight performance bound. The results support our intuition that it is safe to bet more on low-risk options. Surprisingly, the loss bound of the algorithm does not depend on the values of relatively small risks.