Know What You Don't Know: Agentic Data Synthesis by Evolving Generation Space for Closed-Loop Learning

The continued improvement of large language models increasingly depends on synthetic experience, yet effective data synthesis for interactive agents requires not only executable and verifiable trajectories, but also interactions that provide learning value for the current task agent. Existing methods increasingly incorporate environment feedback, data validation, or learner failures, but still face a feedback-to-decision gap: observed weaknesses do not directly specify how future synthesis should change, or whether they can be represented by the current synthesis space. To address this gap, we propose EvoSyn, a learning-feedback-driven multi-agent framework that organizes synthesis around a revisable state specifying what interaction factors can be deliberately generated and where synthesis effort should be allocated. A role-specialized multi-agent system translates learner feedback into synthesis revisions, while a Designer allocates synthesis directions and a Planner grounds them into executable experience. This process enables within-space adaptation toward weak or under-covered regions and synthesis-space expansion that promotes newly discovered factors into explicit generation controls. Experiments on τ squared-Bench and CAR-Bench show that EvoSyn improves average task success by 13.3 points over the strongest synthesis baseline, while producing higher-quality and structurally broader synthetic experience and discovering controllable factors missed without learner feedback.