Before revision:  To do this we generalize the use of adaptive weights pioneered by Hadad et al. (2019) and Deshpande et al. (2018). Specifically, in settings in which the data is collected via a (contextual) bandit algorithm, we prove that certain adaptively weighted M-estimators are uniformly asymptotically normal and demonstrate empirically that we can use their asymptotic distribution to construct reliable confidence regions for a variety of inferential targets.
After revision:  Specifically, we show that M-estimators are uniformly asymptotically normal and demonstrate empirically that we can use their asymptotic distribution to construct reliable confidence regions for a variety of inferential targets.