Query rewriting is a fundamental technique in information retrieval (IR). It typically employs the retrieval result as relevance feedback to refine the query and thereby addresses the vocabulary mismatch between user queries and relevant documents. Traditional pseudo-relevance feedback (PRF) and its vector-based extension (VPRF) improve retrieval performance by leveraging top-retrieved documents as relevance feedback. However, they are constructed based on two major hypotheses: the relevance assumption (top documents are relevant) and the model assumption (rewriting methods need to be designed specifically for particular model architectures). While recent large language models (LLMs)-based generative relevance feedback (GRF) enables model-free query reformulation, it either suffers from severe LLM hallucination or, again, relies on the relevance assumption to guarantee the effectiveness of rewriting quality. To overcome these limitations, we introduce an assumption-relaxed framework: \textit{Generalized Pseudo Relevance Feedback} (GPRF), which performs model-free, natural language rewriting based on retrieved documents, not only eliminating the model assumption but also reducing dependence on the relevance assumption. Specifically, we design a utility-oriented training pipeline with reinforcement learning to ensure robustness against noisy feedback. Extensive experiments across multiple benchmarks and retrievers demonstrate that GPRF consistently outperforms strong baselines, establishing it as an effective and generalizable framework for query rewriting.

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