Distributional Alignment Games for Answer-Level Fine-Tuning
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866909001587884032 |
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| author | Mohri, Mehryar Schneider, Jon Wu, Yifan |
| author_facet | Mohri, Mehryar Schneider, Jon Wu, Yifan |
| contents | We focus on the problem of \emph{Answer-Level Fine-Tuning} (ALFT), where the goal is to optimize a language model based on the correctness or properties of its final answers, rather than the specific reasoning traces used to produce them. Directly optimizing answer-level objectives is computationally intractable due to the need to marginalize over the vast space of latent reasoning paths. To overcome this, we propose a general game-theoretical framework that lifts the problem to a \emph{Distributional Alignment Game}. We formulate ALFT as a two-player game between a Policy (the generator) and a Target (an auxiliary distribution). We prove that the Nash Equilibrium of this game corresponds exactly to the solution of the original answer-level optimization problem. This variational perspective transforms the intractable marginalization problem into a tractable projection problem. We demonstrate that this framework unifies recent approaches to diversity and self-improvement (coherence) and provide efficient algorithms compatible with Group Relative Policy Optimization (GRPO), such as Coherence-GRPO, yielding significant complexity gains in mathematical reasoning tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27166 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distributional Alignment Games for Answer-Level Fine-Tuning Mohri, Mehryar Schneider, Jon Wu, Yifan Machine Learning Computer Science and Game Theory We focus on the problem of \emph{Answer-Level Fine-Tuning} (ALFT), where the goal is to optimize a language model based on the correctness or properties of its final answers, rather than the specific reasoning traces used to produce them. Directly optimizing answer-level objectives is computationally intractable due to the need to marginalize over the vast space of latent reasoning paths. To overcome this, we propose a general game-theoretical framework that lifts the problem to a \emph{Distributional Alignment Game}. We formulate ALFT as a two-player game between a Policy (the generator) and a Target (an auxiliary distribution). We prove that the Nash Equilibrium of this game corresponds exactly to the solution of the original answer-level optimization problem. This variational perspective transforms the intractable marginalization problem into a tractable projection problem. We demonstrate that this framework unifies recent approaches to diversity and self-improvement (coherence) and provide efficient algorithms compatible with Group Relative Policy Optimization (GRPO), such as Coherence-GRPO, yielding significant complexity gains in mathematical reasoning tasks. |
| title | Distributional Alignment Games for Answer-Level Fine-Tuning |
| topic | Machine Learning Computer Science and Game Theory |
| url | https://arxiv.org/abs/2604.27166 |