ChapterZero

A family of optimization problems

July 22nd, 2008 ~ Posted in: Mathematics

We know that $\argmin_x \mathbb{E} \|\phi - x\|_2$ and $\argmin_x \mathbb{E} \|\phi - x\|_1$ are $\mathbb{E}\phi$ and $\text{Med}\phi$ , respectively (assuming the function is nice enough to have a unique median). In general, what is $\argmin_x \mathbb{E} \|\phi - x\|_p$ ?

Mathematics ~

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A family of optimization problems

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