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Timeline for Factorization of argmax

Current License: CC BY-SA 4.0

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Oct 15, 2021 at 16:32 comment added user44143 The notation $a^*_i(s_{n(i)})$ still seems unwieldy and unclear to me — can you give a non-trivial example or two? Also, what conditions on $f$ do you assume to ensure that this and the $\arg \max$’s are unique?
Oct 15, 2021 at 15:56 history edited Minkov CC BY-SA 4.0
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Oct 15, 2021 at 4:37 history edited Minkov CC BY-SA 4.0
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Oct 14, 2021 at 23:31 history edited Minkov CC BY-SA 4.0
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Oct 14, 2021 at 23:29 comment added Minkov @gerw Sorry for the confusion. I have added the requirement that $|n(i)| < p$. Here $a_i^*(s_{n(i)})$ means that the $i$-th coordinate of the argmax only depends on a subset $n(i)$ of the coordinates of $s_{1:p}$.
Oct 14, 2021 at 11:08 comment added gerw It seems that the choice $n(i) \equiv \{1,\ldots,p\}$ is always possible? But maybe I do not understand the definition of $a_i^*(s_{n(i)})$.
Oct 14, 2021 at 7:46 history edited YCor CC BY-SA 4.0
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Oct 14, 2021 at 4:40 history edited Minkov CC BY-SA 4.0
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Oct 14, 2021 at 3:53 history asked Minkov CC BY-SA 4.0