  We generalize active learning to address real-world settings with concrete
prediction targets where sampling is restricted to an accessible region of the
domain, while prediction targets may lie outside this region. We analyze a
family of decision rules that sample adaptively to minimize uncertainty about
prediction targets. We are the first to show, under general regularity
assumptions, that such decision rules converge uniformly to the smallest
possible uncertainty obtainable from the accessible data. We demonstrate their
strong sample efficiency in two key applications: Active few-shot fine-tuning
of large neural networks and safe Bayesian optimization, where they improve
significantly upon the state-of-the-art.
