I do not think that overfitting is “the same thing as” Goodhart’s law. I think Goodhart’s law is more broad. One of the mechanisms by which it works is similar to overfitting, but there is a lot more to Goodhart’s law than overfitting. In particular, I think the standard examples of Goodhart’s law include adversaries that are trying to break your proxy in a way that does not show up in overfitting. See also https://agentfoundations.org/item?id=1621
I do not think that overfitting is “the same thing as” Goodhart’s law. I think Goodhart’s law is more broad. One of the mechanisms by which it works is similar to overfitting, but there is a lot more to Goodhart’s law than overfitting. In particular, I think the standard examples of Goodhart’s law include adversaries that are trying to break your proxy in a way that does not show up in overfitting. See also https://agentfoundations.org/item?id=1621