Suppose $f(x)$ is a concave function and $Y$ is a random variable. What is the relationship between $\arg\max E_Y[\min(f(x),Y)]$ and $\arg\max f(x)$. I feel the former is less than or equal to the latter, but do not have a clue to show it.
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Are you asking about $\max$ or $\arg\max$? – VHarisop Apr 29 '22 at 01:36
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@VHarisop arg max – Justin Apr 30 '22 at 03:14
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I'm not sure if there's anything you could say about the argmax, but your conclusion is definitely true for the max. – VHarisop Apr 30 '22 at 19:59