Budgeted Multi-Hop Retrieval Agent for Compositional Question Answering: A Retrieval-Policy Evaluation on the Official MultiHop-RAG Benchmark

Multi-hop question answering requires a retrieval system to assemble several complementary evidence documents before an answer module can reason reliably. Single-shot retrieval is efficient, but it often misses later-hop evidence when a question combines source, time, comparison, and entity constraints. This paper evaluates a budgeted multi-hop retrieval agent for compositional question answering on the official MultiHop-RAG benchmark. The benchmark contains 2,556 queries and 609 news-article corpus documents, with answerable evidence distributed across two to four documents. Four retrieval policies are compared under the same sparse lexical scorer: fixed top-k retrieval, iterative retrieval, query decomposition, and the proposed budgeted retrieval agent. The revised evaluation frames the task as retrieval-policy evaluation rather than as a full free-form generative QA system: retrieval-conditioned EM/F1 are reported together with evidence recall, MRR, retrieval rounds, selected documents, and context-token cost. On the official data, the budgeted agent achieves the strongest overall retrieval-conditioned EM/F1 at 62.75% and the highest final evidence recall at 74.67%, using 3.011 average retrieval calls and 509.7 average context tokens. Query decomposition improves over fixed top-k and iterative retrieval but is less stable across question types. Fixed top-k is cheapest but incomplete on longer chains. The four-hop results remain difficult for every policy, showing that a fixed 620-token controller should be extended with hop-aware or dynamic budget allocation. The findings support a moderated contribution claim: explicit budget control is useful for auditable multi-hop retrieval, but it should be evaluated as a cost-accuracy trade-off rather than as a universally dominant RAG architecture.