The role of target-specific privilege is investigated with On-Policy Self-Distillation from Other Problems (On-Policy Self-Distillation from Other Problems), which replaces the paired reference with a problem and solution from a different example, while preserving the student rollout, teacher, and distillation objective.
Abstract
On-Policy Self-Distillation (OPSD) is commonly interpreted as the transfer of privileged information: a teacher observes the verified solution to the target problem and supervises the student's trajectory. However, this interpretation conflates two effects. The reference solution not only reveals the answer to the current instance but also changes the context under which the teacher provides token-level supervision. We investigate the role of target-specific privilege with $\mathrm{OP}^{2}\mathrm{SD}$ (On-Policy Self-Distillation from Other Problems), which replaces the paired reference with a problem and solution from a different example, while preserving the student rollout, teacher, and distillation objective. Across three models and three mathematics benchmarks, $\mathrm{OP}^{2}\mathrm{SD}$ improves over the base model, remains competitive with OPSD. The success of $\mathrm{OP}^{2}\mathrm{SD}$ implies that OPSD gains do not necessarily come from access to the reference solution, and that the teacher's context-induced behavior is an important factor.
On-policy self-distillation (OPSD) trains a student on its own responses using token-level supervision from the same model conditioned on privileged reference information. We investigate whether performance gains from OPSD show that the student learned the information in the reference or instead reflect recovery of reasoning behavior already present in the base model. We perform OPSD experiments on science and mathematics datasets using Qwen3 models ranging from 1.7B to 8B. Our analysis framework separates the supervision induced by the reference from the supervision provided by the teacher without the reference and measures how each aligns with changes in the student's predictions. The correct reference does not provide a consistent performance benefit across teacher generation modes, model sizes, and training datasets. Students can improve without the correct reference, and a solution from another problem can outperform the correct solution on several mathematical reasoning benchmarks. The student's predictions align more strongly with the base model's thinking behavior than with the supervision induced by the reference, but controls constructed from other problems reproduce much of both alignments. Moreover, stronger alignment attributable to the correct reference does not reliably coincide with a greater performance benefit from the reference. Performance gains and distributional alignment alone therefore cannot determine how privileged reference information contributes to student learning in OPSD.
Reinforcement learning with verifiable rewards (RLVR) provides reliable outcome supervision for language model reasoning, but a scalar trajectory reward offers limited token-level guidance. Existing self-distillation methods add a privileged teacher but typically assign it a fixed role: direct distribution matching may destabilize successful behavior, while magnitude-only modulation offers little corrective guidance after failure. We observe that successful and failed trajectories require different forms of hindsight supervision. A successful response already contains a valid student-generated reasoning path and can therefore serve as privileged context rather than being replaced by an external rationale. A failed response, however, requires corrective reference information. We introduce Hybrid Hindsight Self-Distillation ($\mathrm{H}^{2}\mathrm{SD}$), which jointly adapts teacher context and update strategy to trajectory correctness. For successful trajectories, we construct the teacher context from the verified response and a rephrasing instruction, and use the teacher only to re-evaluate the original response tokens. The resulting probabilities refine token credit assignment without changing the direction determined by the reward. For failed trajectories, a verified reference hint provides corrective guidance through reverse-KL distillation. Experiments on challenging reasoning benchmarks show that H$^2$SD achieves the strongest overall performance among representative RLVR and self-distillation baselines, with stable optimization and a favorable accuracy-efficiency trade-off.
Qi Cai, Yichuan Ma, Linyang Li et al.· 2 citations
On-policy self-distillation (OPSD) improves the reasoning abilities of LLMs by internalizing privileged context into model parameters through self-distillation. Two recent research lines promote vanilla OPSD by choosing which tokens to learn from and by controlling how much privileged information the teacher receives, respectively. However, we show that each line optimizes one variable while holding the other fixed, which leads to a suboptimal solution. We argue that the two variables are coupled through the student's learning capacity: the privileged information sets the per-token divergence the teacher prescribes, while token weighting selects which of these the student must absorb. We formalize the two lines of work into a unified optimization framework, which maximizes the aggregate teacher--student divergence, subject to a budget on the aggregate learning difficulty the student can absorb. Under this modelling, we propose Unified On-Policy Self-Distillation (USD), a lightweight online algorithm to solve the Lagrangian. USD reveals that a single dual variable governs both decisions: at one price for learning difficulty, it simultaneously sets the token-selection threshold and the direction of privileged-information adjustment, keeping supervision matched to the student's evolving capacity. Through extensive experiments, USD consistently demonstrates superior performance over OPSD and token- and PI-side baselines across various model scales on various reasoning benchmarks. Code is available at https://github.com/lauvlalala/USD.
Yongkang Yang, Zhezheng Hao, Hong Zhang et al.· 0 citations
On-policy self-distillation (OPSD) uses a privileged copy of the student model to provide dense supervision without an external teacher. OPSD keeps this privileged teacher fixed, even though the student distribution and output style change during training. We propose DualOPSD, an asymmetric alternating framework that adapts both policies. The student first learns from the privileged teacher. The teacher then moves toward the updated student distribution on the same student trajectory. This update makes later supervision responsive to the learner and does not require another rollout. On Qwen3-8B in non-thinking mode, DualOPSD improves avg@12 over OPSD by 23.61, 13.89, and 10.00 points on AIME 2024, AIME 2025, and HMMT 2025. Results at 1.7B and 4B show that the accuracy gain depends on model scale. Across all three scales, DualOPSD reduces truncation. The 4B diagnostic also shows lower KL in both directions between the teacher and student.
Yu-Tong Chen, Guangfu Guo, Zhi-Chao Xu et al.· 0 citations
DAPD is proposed, a unified framework with two levels of anchoring that significantly alleviates privilege illusion, outperforming OPSD on Qwen3-4B by +2.00 points on average across tasks.
Jianyu Wu, Yizhou Wang, Encheng Su et al.· 0 citations
Enabling agents to learn from experience and internalize it into their policy has become a central problem in self-evolving AI. On-policy self-distillation (OPSD) offers an effective pathway by using a privileged self-teacher to provide dense supervision on the student's own trajectories; however, existing methods still rely heavily on designer-specified privileged artifacts (e.g., answers, feedback, skills, or trajectories), limiting the end-to-end learnability and scalability required for continual self-improvement. In this work, we introduce Latent On-Policy Self-Distillation (LOPD), which, rather than proposing another hand-crafted OPSD variant with a newly prescribed form of privileged context, makes the teacher's privileged context itself learnable end-to-end from experience. Technically, LOPD retrieves relevant experiences and composes them into continuous latent tokens that condition a self-teacher, while the student generates trajectories from the task and interaction history and receives dense token-level supervision at every visited prefix. We further introduce a privileged-margin objective to stabilize and regulate the learning of latent context. Empirically, LOPD demonstrates (I) strong performance, outperforming RLVR and representative OPSD methods including OPSD, SDPO, and Skill-SD across both agentic tool use and code generation; and (II) high learning efficiency, surpassing GRPO and Skill-SD with less than 30% of their rollout budget. Ablation studies further provide direct evidence that making privileged context learnable is necessary for realizing these gains. Together, these results position LOPD as a step toward a more scalable and self-directed paradigm for agent evolution.
Gui-Min Zhang, Jiayang Lyu, Ran Sun et al.· 0 citations