Symbol M

The passage around this formula

…later gave the phenomenon a formal taxonomy, distinguishing at least four distinct failure mechanisms grouped under Goodhart’s name rather than one [ 1 ] . The simplest to state is regressional: if a proxy metric M relates to the true target U by $M = U + \varepsilon$. for some error term $\varepsilon$ uncorrelated with U , then selecting the run with the highest M selects simultaneously for high U and for large favorable $\varepsilon$ — the optimizer is drawn toward the tail of the error term as reliably as…

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