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Equation 1 · Part 7 · The Main Technical Approaches to AI Alignment, Compared

=

P(yA≻yB∣x)=σ(rϕ(x,yA)−rϕ(x,yB)),P(y_A \succ y_B \mid x) = \sigma\big(r_\phi(x,y_A) - r_\phi(x,y_B)\big),
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

The procedure fits a scalar reward model to pairwise comparisons using the Bradley–Terry choice model, P(yA≻yB∣x)=σ(rϕ(x,yA)−rϕ(x,yB))P(y_A \succ y_B \mid x) = \sigma\big(r_\phi(x,y_A) - r_\phi(x,y_B)\big). then optimizes the policy against that fitted reward under a penalty that keeps it near its starting point,

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.