It seems to me that the discussion on "Extremal Goodhart" is a bunch of good examples of what would be, following your ideas, "Nonlinear Goodhart". It's rather obvious that someone who is 270cm tall has an unusual body that could go either way for basketball, but it's less clear what happens to someone who is 215 cm (when the NBA average is 198cm).
We basically observe correlations "locally", in a neighborhood of the current values. Therefore we think of them as essentially linear, because every smooth function is &... (read more)
It seems to me that the discussion on "Extremal Goodhart" is a bunch of good examples of what would be, following your ideas, "Nonlinear Goodhart". It's rather obvious that someone who is 270cm tall has an unusual body that could go either way for basketball, but it's less clear what happens to someone who is 215 cm (when the NBA average is 198cm).
We basically observe correlations "locally", in a neighborhood of the current values. Therefore we think of them as essentially linear, because every smooth function is &... (read more)