Displacement-Resistant Extensions of DPO with Nonconvex $f$-Divergences
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910014312022016 |
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| author | Pipano, Idan Sabach, Shoham Asadi, Kavosh Ghavamzadeh, Mohammad |
| author_facet | Pipano, Idan Sabach, Shoham Asadi, Kavosh Ghavamzadeh, Mohammad |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_06788 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Displacement-Resistant Extensions of DPO with Nonconvex $f$-Divergences Pipano, Idan Sabach, Shoham Asadi, Kavosh Ghavamzadeh, Mohammad Machine Learning 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. |
| title | Displacement-Resistant Extensions of DPO with Nonconvex $f$-Divergences |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.06788 |