ReBOL: Retrieval via Bayesian Optimization with Batched LLM Relevance Observations and Query Reformulation

LLM-reranking is limited by the top-k documents retrieved by vector similarity, which neither enables contextual query-document token interactions nor captures multimodal relevance distributions. While LLM query reformulation attempts to improve recall by generating improved or additional queries, it is still followed by vector similarity retrieval. We thus propose to address these top-k retrieval stage failures by introducing ReBOL, which 1) uses LLM query reformulations to initialize a multimodal Bayesian Optimization (BO) posterior over document relevance, and 2) iteratively acquires document batches for LLM query-document relevance scoring followed by posterior updates to optimize relevance. After exploring query reformulation and document batch diversification techniques, we evaluate ReBOL against LLM reranker baselines on five BEIR datasets and using two LLMs (Gemini-2.5-Flash-Lite, GPT-5.2). ReBOL consistently achieves higher recall and competitive rankings, for example compared to the best LLM reranker on the Robust04 dataset with 46.5% vs. 35.0% recall@100 and 63.6% vs. 61.2% NDCG@10. We also show that ReBOL can achieve comparable latency to LLM rerankers.