Agentic search augments large language models (LLMs) with external knowledge through reinforcement learning. However, existing approaches suffer from blind reliance on noisy retrieval and hallucination when both parametric and external knowledge fail—reflecting a lack of calibration regarding the model’s knowledge boundary. We propose Knowledge boundary Policy Optimization (KbPO), a reinforcement learning framework that explicitly aligns retrieval decisions with quantified knowledge states. KbPO introduces: (1) a semantic stability metric to delineate reliable parametric knowledge; (2) a four-quadrant taxonomy synthesising internal certainty with retrieval quality; and (3) a quadrant-based reward mechanism incentivising calibrated behaviour. We further adopt an iterative query evolution pipeline to construct boundary-probing training samples. Experiments on ten benchmarks demonstrate that KbPO outperforms strong baselines while exhibiting reduced hallucination rates.

In the pursuit of enhancing domain-specific Large Language Models (LLMs), Retrieval-Augmented Generation (RAG) emerges as a promising solution to mitigate issues such as hallucinations, outdated knowledge, and limited expertise in highly specialized queries. However, existing approaches to RAG fall short by neglecting system state variables, which are crucial for ensuring adaptive control, retrieval halting, and system convergence. In this paper, we introduce the Turing-Complete-RAG (TC-RAG) through rigorous proof, a novel framework that addresses these challenges by incorporating a Turing Complete System to manage state variables, thereby enabling more efficient and accurate knowledge retrieval. By leveraging a memory stack system with adaptive retrieval, reasoning, and planning capabilities, TC-RAG not only ensures the controlled halting of retrieval processes but also mitigates the accumulation of erroneous knowledge via Push and Pop actions. In the case study of the medical and general domain, our extensive experiments on seven real-world healthcare and general-domain datasets demonstrate the superiority of TC-RAG over existing methods in accuracy by over 7.20%. Our code, datasets and RAG resources have been available at https://github.com/Artessay/TC-RAG.