A short note about the learning-augmented secretary problem

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.