When Should Multi-Round RAG Stop? Structured Stopping Judgments and Retrieval Reduction in Search-R1

Multi-round retrieval-augmented generation (RAG) must decide when to stop searching as evidence accumulates. Because the deployed policy is determined by the first STOP on each trajectory, this is a sequential selection problem rather than an independent state-classification task. We adapt S2G-RAG's structured sufficiency-and-gap judgment to a frozen Search-R1 pipeline and train a Qwen3.5-2B judge on 3,009 states from 900 disjoint HotpotQA questions. Search-R1's reasoner, retriever, corpus, prompt, and search budget remain unchanged, while the judge checkpoint and stopping threshold are selected on grouped validation and frozen before confirmatory evaluation. On the confirmatory test set,...

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