Online Allocation with Risk Information

Abstract

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 the Aggregating Algorithm to this problem and give a tight performance bound. The results support our intuition that we should bet more on low-risk options. Surprisingly, however, the Hedge Algorithm without seeing risk information performs nearly as well as the Aggregating Algorithm. So the risk information does not help much. Moreover, the loss bound does not depend on the values of relatively small risks.