We consider a safe optimization problem with bandit feedback in which an agent sequentially chooses actions and observes responses from the environment, with the goal of maximizing an arbitrary function of the response while respecting stage-wise constraints. We propose an algorithm for this problem, and study how the geometric properties of the constraint set impact the regret of the algorithm. In order to do so, we introduce the notion of the sharpness of a particular constraint set, which characterizes the difficulty of performing learning within the constraint set in an uncertain setting. This concept of sharpness allows us to identify the class of constraint sets for which the proposed algorithm is guaranteed to enjoy sublinear regret. Simulation results for this algorithm support the sublinear regret bound and provide empirical evidence that the sharpness of the constraint set impacts the performance of the algorithm.

研究了带有Bandit反馈的安全优化问题，提出了一种针对此问题的算法，探讨了限制集合的几何特性对算法的后悔值的影响。引入了限制集合的尖锐度概念来识别可以保证这个算法后悔值的子线性下界的集合类，并给出了模拟结果支持这一下界，并证明了集合的尖锐度影响了算法的表现。

具有弹奏反馈的安全优化中约束集的几何属性的影响