I've been reading about the secretary problem these days and I got the idea for the case when we know the number of applicants $n$ in advance. I'd like to know what would be an algorithmic approach when this number is unknown and one may have an a priori information about the distribution for the number of applicants.
I found this paper quite interesting because is a multi-attribute extension of the secretary problem and they proposed a dynamic programming method to get the optimal strategy, i.e, when to optimally stop. I implemented it in MATLAB and have an idea. Nevertheless, I have an scenario where one does not know $n$ beforehand. I'd like to tweak this algorithm to make it consider this case.
Thus, my questions are:
What advice do you have to tackle the problem when $n$ is not known? If you have some helpful references, please include them in your answer.
Have you tried to tackle the secretary problem via Linear Programming? If so, how has your experience been?
Do you think the secretary problem optimal strategy could be used to select the best applicants in a real-life setting? I've been reading some papers and people tend to stop too early.
You should read a masterpiece written by Ted Hill
https://www.americanscientist.org/article/knowing-when-to-stop