Before revision:  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 . Then, we introduce and study the Functional Upper Confidence Bound (F-UCB) policy, which interweaves exploration and exploitation and is thus not of the ETC type. Our results show , in particular, that the F-UCB policy (i) performs much better than any ETC policy, and (ii) is near minimax optimal. We also show that a suitably adapted F-UCB policy is near minimax optimal under minimal assumptions when covariate information is available .
After revision:  These are policies, where one initially explores which treatment is of which we show that they are optimal .