Correct — there’s a chance the expected utility quantilizer takes the same action as the expected utility maximizer. That probability is the inverse of the number of actions in the quantile, which is quite small (possibly measure zero) because because actionspace is so large.
Maybe it’s defined like this so it has simpler mathematical properties. Or maybe it’s defined like this because it’s safer. Not sure.
Correct — there’s a chance the expected utility quantilizer takes the same action as the expected utility maximizer. That probability is the inverse of the number of actions in the quantile, which is quite small (possibly measure zero) because because actionspace is so large.
Maybe it’s defined like this so it has simpler mathematical properties. Or maybe it’s defined like this because it’s safer. Not sure.