The researchers introduce AgentGrad, a novel prompt optimization framework designed to enhance the performance of Large Language Model (LLM)-based multi-agent systems (MAS). Addressing critical flaws in existing textual gradient methods—specifically inefficient gradient extraction and suboptimal gradient aggregation—AgentGrad utilizes a two-stage approach involving sequential intervention and semantic abstraction. During the extraction phase, the framework employs sequential intervention to isolate the specific agent responsible for a task failure, ensuring that modifications are applied only to the target agent to provide precise, agent-level supervision. To resolve the issue of mixing unrelated failure modes during aggregation, the method implements semantic textual gradient abstraction, which clusters semantically similar gradients and converts these clusters into generalized corrective patterns. This prevents the generation of conflicting prompts that lack generalization capabilities. Empirical evaluations across five distinct MAS benchmarks demonstrate that AgentGrad achieves state-of-the-art performance. Furthermore, the framework significantly improves computational efficiency, reducing average wall-clock optimization time by 2.5x compared to the next-fastest baseline. By moving beyond random grouping and unverified target selection, AgentGrad provides a more robust and scalable method for optimizing complex multi-agent interactions through fine-grained, semantic feedback.