Large language Models (LLMs) are usually used to answer questions, but many high-stakes applications (e.g., tutoring, clinical support) require the complementary skill of asking questions: detecting missing information, requesting clarifications, and using them to solve tasks. We study this skill in reasoning-heavy domains where progress depends on inquiry rather than factual recall. We define an interactive protocol where a student model engages a stronger teacher under a small turn budget. After each teacher reply, we evaluate the student on the original task with Pass@k. We propose Outcome-Driven Question optimization Strategy (ODQS ), a training framework that learns a questioning policy from downstream task outcomes. At each turn, we sample multiple candidate questions; query the teacher with each, then score the student's resulting performance. Using these scores, we train the student via supervised fine-tuning followed by Direct Preference Optimization (DPO), without any human labels. On GSM8K, HumanEval, and OpenCoder, ODQS produces large gains over interactive baselines, boosting Pass@5 by up to 54.7% (absolute) on math and 22.9% (absolute) on coding, and matching baseline performance in three fewer turns. Thus, question asking can be explicitly trained from task outcomes, improving both accuracy and efficiency in interactive reasoning.
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