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We are provided with a set of $n$ targets. Each target is characterized by a utility value. We know the distribution of the utility value for each target, but do not know its current value. Therefore, we need to probe a target to know its exact current value. We are allowed to probe $m$ out of $n$ targets and will chose one target after probing $m$ targets. We seek the optimal probing strategy that maximizes the expected utility, i.e., the utility of the target we pick at the end.

I would like to know if this problem is related to some known problem.

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This problem is studied. These lecture notes call it the ProbeMax problem: https://faculty.cc.gatech.edu/~ssingla7/courses/Spring22/lec17.pdf

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  • $\begingroup$ thank you! It's indeed useful. $\endgroup$ Commented Sep 17 at 7:08

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