We consider the secretary problem through the lens of learning-augmented algorithms. As it is known that the best possible expected competitive ratio is $1/e$ in the classic setting without predictions, a natural goal is to design algorithms that are 1-consistent and $1/e$-robust. Unfortunately, [FY24] provided hardness constructions showing that such a goal is not attainable when the candidates' true values are allowed to scale with $n$. Here, we provide a simple and explicit alternative hardness construction showing that such a goal is not achievable even when the candidates' true values are constants that do not scale with $n$.

翻译：本文通过学习增强型算法的视角考察秘书问题。已知在无预测的经典设定中，最优期望竞争比为$1/e$，一个自然的目标是设计具有1一致性和$1/e$鲁棒性的算法。遗憾的是，[FY24]通过构造困难实例证明：当候选人的真实价值随$n$增长时，该目标无法实现。本文提出一种简洁且显式的替代困难构造，证明即使候选人的真实价值为不随$n$变化的常数，该目标同样不可实现。