Title:Disentangling Optimization Scale from Preference Scale in DPO

Abstract:Direct Preference Optimization (DPO) is a widely used objective for aligning language models from preference data, with the coefficient $\beta$ commonly interpreted as controlling the KL constraint to a reference policy. We show that $\beta$ entangles two distinct roles: it governs the effective inverse preference-noise scale and simultaneously rescales the optimization dynamics, coupling this scale with the effective step size. As a consequence, at a fixed learning rate the achieved policy deviation is non-monotone in $\beta$: it vanishes in a dead zone at small $\beta$, reaches a peak at an intermediate value, and decreases again for larger $\beta$. Moreover, standard DPO loss values are not comparable across $\beta$: runs with nearly identical loss curves can differ several-fold in KL divergence from the reference model. This entanglement obscures the role of $\beta$, increases sensitivity to hyperparameter choices, and complicates learning-rate scheduling. We propose a centered-softplus reformulation that is argmin-equivalent to DPO for $\beta>0$, while making the inverse preference-noise-scale and learning-rate effects explicit and independently tunable. The normalized centered-softplus objective also admits a continuous $\beta\to0$ endpoint that reduces to a linear preference-margin objective.

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