The theorems are of the form “For all uy, you get good outcomes” or “There exists a uy that causes bad outcomes”.
When you want to prove statements of this form, uy is chosen adversarially, so it matters whether it is chosen before or after R.
uy and R are independently chosen from well-defined distributions.
What distribution is uy chosen from? That’s not specified anywhere in the post.
The theorems are of the form “For all uy, you get good outcomes” or “There exists a uy that causes bad outcomes”.
When you want to prove statements of this form, uy is chosen adversarially, so it matters whether it is chosen before or after R.
What distribution is uy chosen from? That’s not specified anywhere in the post.