Transductive Active Learning with Application to Safe Bayesian Optimization

Abstract

Safe Bayesian optimization (Safe BO) is the task of learning an optimal policy within an unknown environment, while ensuring that safety constraints are not violated. We analyze Safe BO under the lens of a generalization of active learning with concrete prediction targets where sampling is restricted to an accessible region of the domain, while prediction targets may lie outside this region. We study a family of policies that sample adaptively to minimize uncertainty about prediction targets. We are the first to show, under general regularity assumptions, that such policies converge uniformly to the smallest possible uncertainty obtainable from the accessible data. Leveraging this result, we apply our framework to Safe BO and demonstrate that our decision rules improve substantially upon the state-of-the-art.