Before revision:  In the present article, we evaluate assignment policies according to their regret, that is, the sum of all losses incurred due to assigning subjects to suboptimal treatments. We first study explore-then-commit (ETC) policies. These are policies, where one initially explores which treatment is of the highest quality, typically through a randomized controlled trial, and subsequently fully commits to the ``inferred superior'' (but potentially suboptimal) treatment .
After revision:  In the present paper we introduce and study sequential learning algorithms when the distributional characteristic of interest is a general functional of the outcome distribution. In particular, it turns out that intuitively reasonable approaches, such as first conducting an experiment on an initial group of subjects followed by rolling out the inferred best treatment to the population, are dominated by the policies we develop and of the highest quality, typically through a randomized controlled trial, and subsequently fully commits to the ``inferred superior'' (but potentially suboptimal) treatment .