Right, that’s the question. Sure, it is easy to state that “metric must be a faithful representation of the target”, but it never is, is it? From the point of view of double inversion, optimizing the target is a hard inverse problem, because, like in your pizza example, the true “values” (pizza is a preference on the background of an otherwise balanced diet) is not easily observable. What would be a double inverse in this case? Maybe something like trying various amounts of pizza and getting the feedback on enjoyment? That would match the long division pattern. I’m not sure.
Right, that’s the question. Sure, it is easy to state that “metric must be a faithful representation of the target”, but it never is, is it? From the point of view of double inversion, optimizing the target is a hard inverse problem, because, like in your pizza example, the true “values” (pizza is a preference on the background of an otherwise balanced diet) is not easily observable. What would be a double inverse in this case? Maybe something like trying various amounts of pizza and getting the feedback on enjoyment? That would match the long division pattern. I’m not sure.