用生成伪文档替代重写查询，让大模型更高效地提升检索效果。

Recent advances in large language models (LLMs) have led to a surge of interest in query augmentation for information retrieval (IR). Two main approaches have emerged. The first prompts LLMs to generate answers or pseudo-documents that serve as new queries, relying purely on the model's parametric knowledge or contextual information. The second applies reinforcement learning (RL) to fine-tune LLMs for query rewriting, directly optimizing retrieval metrics. While having respective advantages and limitations, the two approaches have not been compared under consistent experimental conditions. In this work, we present the first systematic comparison of prompting-based and RL-based query augmentation across diverse benchmarks, including evidence-seeking, ad hoc, and tool retrieval. Our key finding is that under a compute-aware comparison setting, simple, training-free query augmentation often performs on par with, or even surpasses, more expensive RL-based counterparts, especially when using powerful LLMs. Motivated by this discovery, we introduce a novel hybrid method, On-policy Pseudo-document Query Expansion (OPQE), in which the LLM policy learns to generate a pseudo-document that maximizes retrieval performance, rather than rewriting the query, thus merging the flexibility and generative structure of prompting with the targeted optimization of RL. We show OPQE outperforms both standalone prompting and RL-based rewriting, demonstrating that a synergistic approach yields the best results. We open source our implementation to facilitate reproducibility.