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：我们通过学习增强算法的视角来考察秘书问题。众所周知，在无预测的经典设定下，最佳可能的期望竞争比为$1/e$，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]给出了困难性构造，表明当候选人的真实价值允许随$n$缩放时，这一目标无法实现。在此，我们提供了一个简单且显式的替代困难性构造，表明即使候选人的真实价值为不随$n$缩放的常数，该目标同样无法达成。