  The value maximization version of the secretary problem is the problem of
hiring a candidate with the largest value from a randomly ordered sequence of
candidates. In this work, we consider a setting where predictions of candidate
values are provided in advance. We propose an algorithm that achieves a nearly
optimal value if the predictions are accurate and results in a constant-factor
competitive ratio otherwise. We also show that the worst-case competitive ratio
of an algorithm cannot be higher than some constant $< 1/\mathrm{e}$, which is
the best possible competitive ratio when we ignore predictions, if the
algorithm performs nearly optimally when the predictions are accurate.
Additionally, for the multiple-choice secretary problem, we propose an
algorithm with a similar theoretical guarantee. We empirically illustrate that
if the predictions are accurate, the proposed algorithms perform well;
meanwhile, if the predictions are inaccurate, performance is comparable to
existing algorithms that do not use predictions.
