Rethinking Reinforcement Fine-Tuning in LVLM: Convergence, Reward Decomposition, and Generalization

• URL: http://arxiv.org/abs/2604.19857v1
• Date: Tue, 21 Apr 2026 17:21:08 GMT
• Title: Rethinking Reinforcement Fine-Tuning in LVLM: Convergence, Reward Decomposition, and Generalization
• Abstract summary: 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.<n>Despite striking empirical successes, most notably Visual Agentic Reinforcement Fine-Tuning (Visual-ARFT), the theoretical underpinnings of this paradigm remain poorly understood.<n>We introduce the emphTool-Augmented Markov Decision Process (TA-MDP), a formal framework that models multimodal agentic decision-making with bounded-depth tool calls.
• Score: 3.579200789027982
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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}).

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