Asymptotically Optimal Sequential Capital Allocation Strategies

Abstract

Nearly all of the current literature on multi-armed bandits has been dedicated to maximizing the expected sum of samples from a set of distributions. However, it may be more desirable to prioritize risk management in some applications. In this thesis, we propose a new variant of the multi-armed bandit problem that is based on the Kelly Criterion, which derives motivation from portfolio optimization and exhibits desirable risk management properties. We introduce novel algorithms to solve this variant and prove theoretical bounds on the performance of theses algorithms.