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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.19857 |
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| _version_ | 1866918460994355200 |
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| author | Adams, Carter Oliveira, Rafael Almeida, Gabriel Torres, Sofia |
| author_facet | Adams, Carter Oliveira, Rafael Almeida, Gabriel Torres, Sofia |
| contents | Reinforcement fine-tuning with verifiable rewards (RLVR) has emerged as a powerful paradigm for equipping large vision-language models (LVLMs) with agentic capabilities such as tool use and multi-step reasoning. Despite striking empirical successes, most notably Visual Agentic Reinforcement Fine-Tuning (Visual-ARFT), the theoretical underpinnings of this paradigm remain poorly understood. In particular, two critical questions lack rigorous answers: (i)~how does the composite structure of verifiable rewards (format compliance, answer accuracy, tool executability) affect the convergence of Group Relative Policy Optimization (GRPO), and (ii)~why does training on a small set of tool-augmented tasks transfer to out-of-distribution domains? We address these gaps by introducing the \emph{Tool-Augmented Markov Decision Process} (TA-MDP), a formal framework that models multimodal agentic decision-making with bounded-depth tool calls. Within this framework, we establish three main results. First, we prove that GRPO under composite verifiable rewards converges to a first-order stationary point at rate $O(1/\sqrt{T})$ with explicit dependence on the number of reward components and group size (\textbf{Theorem~1}). Second, we derive a \emph{Reward Decomposition Theorem} that bounds the sub-optimality gap between decomposed per-component optimization and joint optimization, providing a precise characterization of when reward decomposition is beneficial (\textbf{Theorem~2}). Third, we establish a PAC-Bayes generalization bound for tool-augmented policies that explains the strong out-of-distribution transfer observed in Visual-ARFT (\textbf{Theorem~3}). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19857 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rethinking Reinforcement Fine-Tuning in LVLM: Convergence, Reward Decomposition, and Generalization Adams, Carter Oliveira, Rafael Almeida, Gabriel Torres, Sofia Machine Learning Computation and Language Reinforcement fine-tuning with verifiable rewards (RLVR) has emerged as a powerful paradigm for equipping large vision-language models (LVLMs) with agentic capabilities such as tool use and multi-step reasoning. Despite striking empirical successes, most notably Visual Agentic Reinforcement Fine-Tuning (Visual-ARFT), the theoretical underpinnings of this paradigm remain poorly understood. In particular, two critical questions lack rigorous answers: (i)~how does the composite structure of verifiable rewards (format compliance, answer accuracy, tool executability) affect the convergence of Group Relative Policy Optimization (GRPO), and (ii)~why does training on a small set of tool-augmented tasks transfer to out-of-distribution domains? We address these gaps by introducing the \emph{Tool-Augmented Markov Decision Process} (TA-MDP), a formal framework that models multimodal agentic decision-making with bounded-depth tool calls. Within this framework, we establish three main results. First, we prove that GRPO under composite verifiable rewards converges to a first-order stationary point at rate $O(1/\sqrt{T})$ with explicit dependence on the number of reward components and group size (\textbf{Theorem~1}). Second, we derive a \emph{Reward Decomposition Theorem} that bounds the sub-optimality gap between decomposed per-component optimization and joint optimization, providing a precise characterization of when reward decomposition is beneficial (\textbf{Theorem~2}). Third, we establish a PAC-Bayes generalization bound for tool-augmented policies that explains the strong out-of-distribution transfer observed in Visual-ARFT (\textbf{Theorem~3}). |
| title | Rethinking Reinforcement Fine-Tuning in LVLM: Convergence, Reward Decomposition, and Generalization |
| topic | Machine Learning Computation and Language |
| url | https://arxiv.org/abs/2604.19857 |