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However, we identify a critical limitation: when the student and teacher distributions diverge significantly, standard RKL often fails to yield meaningful improvement due to uninformative negative feedback. To address this inefficiency, we propose Teacher-Guided Policy Optimization (TGPO), an on-policy algorithm that incorporates dense directional guidance by leveraging teacher predictions conditioned on the student's rollout. Because TGPO remains on-policy, the algorithm integrates seamlessly with existing RLVR frameworks without requiring additional data annotation. 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Because TGPO remains on-policy, the algorithm integrates seamlessly with existing RLVR frameworks without requiring additional data annotation. 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