TeachBack: Learning to Teach via Bidirectional Preference Optimization for On-Policy Self-Distillation

On-policy self-distillation (OPSD) enables a language model to learn from a Teacher instantiated from the same model but given access to privileged information, such as a reference solution. We find that access to sufficient privileged information allows the Teacher to generate highly accurate trajectories; however, accuracy alone does not guarantee that these trajectories are suitable for Student learning. Direct access to a complete solution may encourage shortened, reference-conditioned derivations that omit the exploration, verification, and self-correction required to solve problems without privileged information. We introduce TeachBack, a bidirectional preference-learning framework for on-policy self-distillation that learns not only from the Teacher but also how the Teacher should teach. TeachBack shapes the Teacher's generation behavior by controlling the length of the reference-reasoning suffix injected into the prompt and by varying the prompt style. While maintaining comparable Teacher accuracy, it encourages the Teacher to explore and re-solve problems, thereby reducing its reliance on the reference solution. At each rollout refresh, the shared policy generates both a privileged Teacher trajectory and a problem-only Student trajectory. A pairwise preference objective uses privileged Teacher trajectories to improve Student learning, while the reversed preference uses the Student's behavior to shape future Teacher supervision under the privileged condition. Experiments on mathematical and logical reasoning tasks show that TeachBack consistently improves Student performance over existing OPSD methods and related baselines.