Group-relative residual calibration can incorporate verifier outcomes without discarding dense token-level guidance, and demonstrates that group-relative residual calibration can incorporate verifier outcomes without discarding dense token-level guidance.
Abstract
On-policy distillation (OPD) trains a student on its own responses using dense token-level guidance from a stronger teacher. In long-context tasks, however, token-level teacher support can favor locally plausible responses that omit evidence distributed across the input or violate global task constraints. Task-specific verifiers, in contrast, evaluate task completion at the response level and may return graded rewards that reflect partial success. We diagnose this mismatch on fixed responses from two representative long-context evidence-aggregation tasks. Across longer input ranges, trajectory-level OPD scores become progressively less aligned with verifier rewards, indicating teacher-verifier disagreement. Motivated by this observation, we introduce Group-Calibrated On-Policy Distillation (GC-OPD). GC-OPD separately normalizes verifier rewards and trajectory-level OPD scores within each rollout group and uses their difference as a signed teacher-verifier disagreement residual. Relative-advantage-based credit assignment (RACA) distributes this trajectory-level residual across tokens according to their relative OPD advantages while preserving the original OPD signal. Across five long-context benchmarks, post-training with GC-OPD raises the five-benchmark averages of the official Qwen3-4B and Qwen3-8B checkpoints from 29.08 to 40.47 and from 35.12 to 44.65, respectively. Vanilla OPD reaches 39.31 and 43.56 under the same setup. Controlled ablations show that the signed residual is more effective than either an additional OPD-derived term or direct group-normalized verifier reward addition, while RACA further improves over uniform token allocation. Together, these results demonstrate that group-relative residual calibration can incorporate verifier outcomes without discarding dense token-level guidance. Code is available at https://github.com/SolereZhang/GC-OPD.
On-policy distillation is a powerful way to transfer reasoning ability from a strong teacher to a smaller student: the student samples trajectories from its own policy, and the teacher provides dense token-level supervision on the states the student actually visits. However, this supervision is not always reliable: a teacher can assign high likelihood to plausible but incorrect solutions, or low likelihood to correct student solutions that follow different reasoning paths. Unconditionally distilling the teacher can therefore reinforce bad modes or erase useful student behavior. To address these limitations, we introduce RG-OPD: Reward-Gated On-Policy Distillation that uses verifier feedback to decide when teacher logits should be trusted. RG-OPD bridges sparse verifier rewards and dense teacher logits, preserving token-level supervision while filtering misleading teacher signals. Across reasoning and coding benchmarks, RG-OPD produces stronger distilled students, outperforming both vanilla reverse-KL distillation and the recent TSD-KD baseline. At 1K generation length, RG-OPD improves over reverse-KL by 2.9 points and over TSD-KD by 4.9 points; in the long-generation setting, it improves over the untuned student by 8.2 points. Our code is available at https://github.com/UoC-tail/RG-OPD.
Mohammad Sadegh Akhondzadeh, Vijay Lingam, Atula Tejaswi et al.· 2 citations
Reinforcement learning with verifiable rewards yields no group-relative signal when rollout groups are uniformly correct or uniformly wrong, which account for 63.0-68.0% of groups in our experiments. We propose SKALD (Skill-Anchored Latent Distillation), an on-policy self-distillation framework that uses two context views of the same Qwen3-Base model: a question-only student and a teacher conditioned on an abstract, explicit-answer-filtered skill card. The student is trained on its own prefixes, transferring the skill-induced advantage into shared parameters without privileged input at test time. To stabilize context-induced distribution mismatch, SKALD employs an annealed exponentially tilted objective that downweights teacher-preferred tokens with very low student likelihood; as the tilt vanishes, it converges to teacher cross-entropy and recovers the forward-KL student gradient. An empirical gate activates distillation only when verified rollouts estimate a positive teacher advantage. Across five held-out mathematics benchmarks, SKALD improves overall avg@8 over GRPO by +2.46, +4.85, and +12.01 at 0.6B, 1.7B, and 4B, respectively. At 1.7B, zero-variance-only distillation recovers 84.7% of the full gain, while SKALD remains +4.06 above FLOP-matched GRPO and exceeds contextual skill exposure by +3.77. These results show that abstract skills provide dense supervision where group-relative rewards become uninformative.
Yubo Jiang, Feng-ying Xie, Zhiguo Jiang et al.· 0 citations
On-policy self-distillation aims to improve upon reinforcement learning from verifiable rewards (RLVR) by providing token-level scores derived from privileged information, such as reference solutions or critic feedback. These scores are treated as estimates of token-level action values, yet they answer a fundamentally different question: how the model's prediction changes when its input context is enriched, rather than how the expected outcome changes when a token is changed. We examine this gap along three dimensions: (i) whether the token-level score tracks task success; (ii) whether feedback generated from the same rollout causes the score to reflect agreement with its own description, and whether using feedback from other rollouts in the group mitigates this self-referential effect; and (iii) what behavior the resulting training objective actually reinforces. In experiments on AIME 2025, the implemented score distinguishes correct from incorrect rollouts at approximately chance level (AUC=0.505); using feedback from a different rollout does not consistently improve this discrimination; and all training configurations achieve only 24.2-33.9% Avg@4, compared with 64.2% for outcome-only GRPO. Moreover, the highest-entropy token decile accounts for 57-71% of the total absolute token-advantage mass, despite the score being least informative about reasoning quality in this regime. By contrast, similar experiments on SciKnowEval Biology improves held-out Avg@8 by 28.0%, while its corresponding trajectory scores achieve AUCs of 0.81-0.92. Together, these results suggest that dense credit assignment through distillation can be effective when its likelihood-based scores are empirically validated as meaningful proxies for outcome-relevant credit. When this alignment does not hold, however, the resulting supervision can fail to generalize and may substantially underperform outcome-based RL.
Xuan-Phi Nguyen, Shrey Pandit, Yiran Zhao et al.· 1 citation
Reinforcement learning with verifiable rewards (RLVR) offers a verifier-bounded performance ceiling for training multi-turn tool-use agents, yet its trajectory-level credit assignment conflates heterogeneous per-turn outcomes into a single reward signal. On-policy distillation provides dense per-token supervision but is either teacher-bounded or prone to gradient concentration collapse. We introduce $\textbf{CrEST}$, a hierarchical credit assignment framework that retains RL's verifier-bounded ceiling while incorporating dense token-level signals from a privileged self-teacher. $\textbf{CrEST}$ resolves credit at two levels: turn-segmented verified advantages address inter-turn dilution, while entropy-gated self-teacher modulation refines intra-turn token contributions. Experiments on BFCL V3 and WildToolBench show that $\textbf{CrEST}$ consistently outperforms both RL and distillation baselines across two model scales, with the largest gains on long-trajectory and strict session-level metrics. Our work demonstrates that the teacher's role in policy optimization can be reduced from determining update directions to modulating update magnitudes, unlocking dense credit assignment without sacrificing the verifier-bounded ceiling.
Zechuan Wang, Siyuan Lu, Hongxuan Zhang et al.· 0 citations
On-policy distillation (OPD) has emerged as an effective framework for post-training language models by pairing student-generated trajectories with dense token-level supervision from a teacher. However, OPD implicitly assumes that teacher-derived rewards are an appropriate proxy for reasoning progress, and therefore treats all teacher feedback equally during policy optimization. While in practice, this assumption does not always hold. We observe that teacher-derived rewards often conflict with genuine reasoning progress, as reasoning steps with clear reasoning advancement may still receive lower distillation rewards, simply due to deviation from teacher's outputs. To address this mismatch, we propose Reasoning-Progress-Aware Reward Filtering for On-Policy Distillation (R2-OPD), which constructs two within-trajectory rankings of reasoning spans, one from teacher-derived rewards and the other from independently estimated progress reward. Distillation rewards are selectively suppressed whenever the two rankings disagree, reducing supervision that conflicts with reasoning progress while preserving effective teacher guidance. Our approach shows consistent improvement over standard OPD especially regarding reasoning performances.
Cheng Yang, Haiyuan Wan, Rengrong Xiong et al.· 0 citations
On-policy distillation (OPD) trains a student on its own trajectories under dense token-level supervision from a teacher. Reward-extrapolation methods such as ExOPD amplify the teacher-reference log-likelihood ratio to move beyond direct imitation, but apply a single global coefficient $\lambda$ to every token. This can drive the student to fit extreme peaks in the implicit reward, causing reward hacking and unstable training, and the optimal $\lambda$ varies across domains, requiring costly sweeps. We propose REOPD, a reliability-adaptive reward extrapolation framework for OPD. REOPD combines a token-level compatibility weight with a batch-level adaptive budget, yielding a token-wise coefficient $\lambda_{b,t}=1+\gamma_b q_t$ that preserves teacher alignment while selectively extrapolating along reliable teacher-reference directions. It requires no verifier, reward model, value model, or extra rollout beyond standard OPD. REOPD outperforms G-OPD on single-teacher mathematics and on both domains in the multi-teacher setting, while matching G-OPD on single-teacher code, demonstrating effective fine-grained reliability adaptation across domains and teacher configurations.
Yang Sun, Lichao Ma, Houyuan Qin et al.· 0 citations
A new machine-learning framework aims to improve the success rate of computational protein design while moving away from results that reproduce sequences found in nature.
