Equation 3 · Part 2 · Ten Ways an Agent Evaluation Can Mislead You Even When It's Working Correctly
Symbol U
What this part means
the highest m selects simultaneously for high.
Its job in the formula
U is one of the signed contributions combined to compute the quantity on the left.
Full expression→Symbol U→Article meaning
Where the article explains it
for some error term uncorrelated with U , then selecting the run with the highest M selects simultaneously for high U and for large favorable — the optimizer is drawn toward the tail of the error term as reliably as toward genuine capability, and the more intensely M is optimized, the larger a share of the observed gain is rather than U .
The passage around this formula
…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 . for some error term uncorrelated with U , then selecting the run with the highest M selects simultaneously for high U and for large favorable — the optimizer is drawn toward the tail of the error term as reliably as toward genuine capability, and…
Learn the underlying idea
A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
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Sources cited in the surrounding passage
- [2] 'Improving ratings': audit in the British University system ↗
- [1] Categorizing Variants of Goodhart's Law ↗
These citations provide research context; check each source for the exact claim it supports.