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 policies improve substantially upon the state-of-the-art.

@inproceedings{hubotter2024transductive2,
  title={Transductive Active Learning with Application to Safe Bayesian Optimization},
  author={H{\"u}botter, Jonas and Sukhija, Bhavya and Treven, Lenart and As, Yarden and Krause, Andreas},
  booktitle = {ICML 2024 Workshop on Aligning Reinforcement Learning Experimentalists and Theorists},
  year={2024},
  pdf={https://jonhue.github.io/assets/pdf/icml-2024-arlet.pdf}}