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Equation 2 · Part 3 · The Main Technical Approaches to AI Alignment, Compared

Symbol r_phi

max⁡θ  Ex, y∼πθ[rϕ(x,y)]  −  β DKL(πθ ∥ πref).\max_\theta \; \mathbb{E}_{x,\, y\sim\pi_\theta}\big[r_\phi(x,y)\big] \;-\; \beta \, D_{\mathrm{KL}}\big(\pi_\theta \,\Vert\, \pi_{\mathrm{ref}}\big).
rϕr_\phi

What this part means

rpr_phi is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

rpr_phi is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

…under a penalty that keeps it near its starting point, max⁡θ  Ex, y∼πθ[rϕ(x,y)]  −  β DKL(πθ ∥ πref)\max_\theta \; \mathbb{E}_{x,\, y\sim\pi_\theta}\big[r_\phi(x,y)\big] \;-\; \beta \, D_{\mathrm{KL}}\big(\pi_\theta \,\Vert\, \pi_{\mathrm{ref}}\big). Read the two equations together and the oversight limit is visible in the structure itself, not only in later critiques of it. The reward model rϕr_\phi is trained on whatever a human rater could see and judge in the time given; nothing forces it to track truth or usefulness beyond what raters could distinguish. The KL term in the second equation is a standing admission of that limit — it constrains how far the policy may travel from the…

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