In the Retrieval-Augmented Generation (RAG) system, advanced Large Language
Models (LLMs) have emerged as effective Query Likelihood Models (QLMs) in an
unsupervised way, which re-rank documents based on the probability of
generating the query given the content of a document. However, directly
prompting LLMs to approximate QLMs inherently is biased, where the estimated
distribution might diverge from the actual document-specific distribution. In
this study, we introduce a novel framework, $\mathrm{UR^3}$, which leverages
Bayesian decision theory to both quantify and mitigate this estimation bias.
Specifically, $\mathrm{UR^3}$ reformulates the problem as maximizing the
probability of document generation, thereby harmonizing the optimization of
query and document generation probabilities under a unified risk minimization
objective. Our empirical results indicate that $\mathrm{UR^3}$ significantly
enhances re-ranking, particularly in improving the Top-1 accuracy. It benefits
the QA tasks by achieving higher accuracy with fewer input documents.

利用贝叶斯决策理论提出的 UR^3 框架有效地改进了 Retrieval-Augmented Generation 系统的 Top-1 准确率，通过最大化文档生成的概率在统一的风险最小化目标下优化查询和文档生成概率。