This relates here: https://math.stackexchange.com/questions/1820997/why-is-the-classical-secretary-problem-about-ranks
You want to stop optimal in a sequence of items presented sequentially, that is you want to stop at the maximum. The distribution of these items is unknown. If the distribution was known exactly the best stopping rule would give winning probability 0.58 or better.
CLAIM:
If nothing is known the best strategy is to restrict to the relative of the items seen and then this is equivalent to the classical secretary problem.
This seems very clear - but I find myself unable to prove it.
If the possible distributions were a locally compact group this would do the job but they are not. https://projecteuclid.org/euclid.aoms/1177706874
Any help is much appreciated.
Best Regards
