We introduce the safe best-arm identification framework with linear feedback,
where the agent is subject to some stage-wise safety constraint that linearly
depends on an unknown parameter vector. The agent must take actions in a
conservative way so as to ensure that the safety constraint is not violated
with high probability at each round. Ways of leveraging the linear structure
for ensuring safety has been studied for regret minimization, but not for
best-arm identification to the best our knowledge. We propose a gap-based
algorithm that achieves meaningful sample complexity while ensuring the
stage-wise safety. We show that we pay an extra term in the sample complexity
due to the forced exploration phase incurred by the additional safety
constraint. Experimental illustrations are provided to justify the design of
our algorithm.

介绍了具有线性反馈的安全最优臂识别框架，代理受到一些在未知参数向量上线性相关的逐阶段安全约束的限制，代理必须以保守的方式采取行动，以确保在每一轮中不违反安全约束的概率较高。提出了一种基于间隙的算法，实现了有意义的样本复杂度，同时确保逐阶段的安全性。通过实验说明了算法设计的合理性。