This paper proposes the Reinforced Inference Augmentation Generation (ReinRAG) model, which aims to generate long-form discharge instructions from limited patient information. ReinRAG provides explicit semantic guidance to the LLM by searching inference paths in the medical knowledge graph. To address information gaps, we propose group-based retrieval optimization (GRO) to improve retrieval quality with group-normalized rewards and encourage inference leaps for deep inference in the LLM. Experimental results on real-world datasets demonstrate that ReinRAG outperforms existing methods in both clinical effectiveness and natural language generation metrics. Further analysis demonstrates that ReinRAG bridges semantic gaps in insufficient input and ensures that the retrieved inference paths focus on key evidence and follow consistent inferences, thereby preventing clinical misinterpretation in the LLM.