Displacement-Resistant Extensions of DPO with Nonconvex $f$-Divergences

• URL: http://arxiv.org/abs/2602.06788v1
• Date: Fri, 06 Feb 2026 15:45:37 GMT
• Title: Displacement-Resistant Extensions of DPO with Nonconvex $f$-Divergences
• Abstract summary: DPO and related algorithms align language models by directly optimizing the RLHF objective.<n>We show that DPO-inducing characterizes when the RLHF problem remains tractable.<n>We then focus on a specific DPO-inducing and displacement-resistant $f$, leading to our novel SquaredPO loss.
• Score: 23.894803166231792
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: DPO and related algorithms align language models by directly optimizing the RLHF objective: find a policy that maximizes the Bradley-Terry reward while staying close to a reference policy through a KL divergence penalty. Previous work showed that this approach could be further generalized: the original problem remains tractable even if the KL divergence is replaced by a family of $f$-divergence with a convex generating function $f$. Our first contribution is to show that convexity of $f$ is not essential. Instead, we identify a more general condition, referred to as DPO-inducing, that precisely characterizes when the RLHF problem remains tractable. Our next contribution is to establish a second condition on $f$ that is necessary to prevent probability displacement, a known empirical phenomenon in which the probabilities of the winner and the loser responses approach zero. We refer to any $f$ that satisfies this condition as displacement-resistant. We finally focus on a specific DPO-inducing and displacement-resistant $f$, leading to our novel SquaredPO loss. Compared to DPO, this new loss offers stronger theoretical guarantees while performing competitively in practice.

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