Enforcing safety is a key aspect of many problems pertaining to sequential decision making under uncertainty, which require the decisions made at every step to be both informative of the optimal decision and also safe. For example, we value both efficacy and comfort in medical therapy, and efficiency and safety in robotic control. We consider this problem of optimizing an unknown utility function with absolute feedback or preference feedback subject to unknown safety constraints. We develop an efficient safe Bayesian optimization algorithm, StageOpt, that separates safe region expansion and utility function maximization into two distinct stages. Compared to existing approaches which interleave between expansion and optimization, we show that StageOpt is more efficient and naturally applicable to a broader class of problems. We provide theoretical guarantees for both the satisfaction of safety constraints as well as convergence to the optimal utility value. We evaluate StageOpt on both a variety of synthetic experiments, as well as in clinical practice. We demonstrate that StageOpt is more effective than existing safe optimization approaches, and is able to safely and effectively optimize spinal cord stimulation therapy in our clinical experiments.

本研究针对优化未知效用函数的绝对或偏好反馈时的安全性约束问题，提出了一种有效的安全贝叶斯优化算法 StageOpt，并通过理论和临床实验验证了 StageOpt 在扩展安全区域和最大化效用函数两个阶段上的高效性和效果优于现有方法的特点。

阶段安全的高斯过程贝叶斯优化