Multimodal Large Language Models (MLLMs) face significant scalability challenges in long-video understanding due to quadratic attention complexity and context window constraints. Existing retrieval-based approaches typically rely on supervised learning from static keyframe annotations. However, these label priors often fail to align with the actual information required by downstream MLLMs for complex reasoning, creating a misalignment between the training target and inference needs. To bridge this gap, we propose a probabilistic framework that reformulates frame selection as latent-variable inference. We first initialize a lightweight policy using supervised learning to capture general visual saliency. Then, we treat a frozen MLLM as a task environment and use its answer likelihood as dense task evidence to refine the policy via Bayesian Group Relative Policy Optimization (GRPO). Within this formulation, the negative log-likelihood (NLL) over ground-truth answer tokens provides a principled dense reward, while a prior-matching KL term preserves semantic consistency with the elicited label prior. This process transitions the selection principle from static label priors to task evidence. Extensive experiments on Video-MME, MLVU, and LongVideoBench demonstrate that our selector achieves competitive accuracy with MLLM-based scorers while retaining the inference efficiency of lightweight methods. The selector is trained once with a frozen MLLM environment and transfers directly to multiple downstream MLLMs without retraining. Code is available at github.com/Miraclecsc/Frame_Selection_GRPO

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