While Large Language Models (LLMs) exhibit exceptional zero-shot relevance modeling, their high computational cost necessitates framing passage retrieval as a budget-constrained global optimization problem. Existing approaches passively rely on first-stage dense retrievers, which leads to two limitations: (1) failing to retrieve relevant passages in semantically distinct clusters, and (2) failing to propagate relevance signals to the broader corpus. To address these limitations, we propose Bayesian Active Learning with Gaussian Processes guided by LLM relevance scoring (BAGEL), a novel framework that propagates sparse LLM relevance signals across the embedding space to guide global exploration. BAGEL models the multimodal relevance distribution across the entire embedding space with a query-specific Gaussian Process (GP) based on LLM relevance scores. Subsequently, it iteratively selects passages for scoring by strategically balancing the exploitation of high-confidence regions with the exploration of uncertain areas. Extensive experiments across four benchmark datasets and two LLM backbones demonstrate that BAGEL effectively explores and captures complex relevance distributions and outperforms LLM reranking methods under the same LLM budget on all four datasets.

翻译：尽管大型语言模型在零样本相关性建模方面表现出色，但其高昂的计算成本使得段落检索必须被建模为预算受限的全局优化问题。现有方法被动依赖第一阶段的稠密检索器，导致两个局限：（1）无法检索语义上分散的不同簇中的相关段落，（2）无法将相关性信号传播到更广泛的语料库。为解决这些问题，我们提出基于LLM相关性评分的高斯过程贝叶斯主动学习框架（BAGEL），该框架通过将稀疏的LLM相关性信号沿嵌入空间传播，引导全局探索。BAGEL基于LLM相关性评分，利用查询特定的高斯过程对整个嵌入空间中的多模态相关性分布进行建模，随后通过战略性地平衡高置信度区域的利用与不确定区域的探索，迭代选择待评分的段落。在四个基准数据集和两个LLM主干上的大量实验表明，BAGEL能够有效探索并捕获复杂的相关性分布，且在相同LLM预算下，在所有四个数据集上的表现均优于LLM重排序方法。