Functional Sequential Treatment Allocation

Consider a setting in which policy maker assigns subjects to treatments, observing each outcome before the next subject arrives. Initially, it is unknown treatment best, but sequential nature of problem permits learning about effectiveness treatments. While multi-armed-bandit literature has shed much light on situation when compares treatments through their mean, less known other targets. This restrictive, because cautious decision may prefer target robust location measure such as quantile or trimmed mean. Furthermore, socio-economic making often requires targeting purpose specific characteristics distribution, its inherent degree inequality, welfare poverty. In present article, we introduce and study algorithms distributional characteristic interest general functional distribution. Minimax expected regret optimality results are obtained within subclass explore-then-commit policies, for unrestricted class all policies. Supplementary materials this article available online.