Multi-constraint instruction following requires a model to respond to a query under many simultaneously active constraints. Even strong instruction-tuned models still routinely violate some of them. Existing approaches either augment supervision with sequence- or token-level RL rewards from external verifiers or learned graders, or use on-policy distillation (OPD) against a single full-context teacher whose probability mass becomes diluted as more constraints become simultaneously active. We propose CC-OPD (Counterfactual Constraint-Conditioned On-Policy Distillation), which inverts the standard supervision-generation direction in distillation. Rather than enriching the teacher with information beyond what the student sees, CC-OPD ablates each constraint from the teacher's conditioning in turn, and constructs the per-constraint signal from the resulting per-token probability differentials. The resulting per-token leave-one-out log-likelihood shifts are summed, clipped, and added to the vanilla OPD reward as a token-level shaping term. All shaping terms are obtained from the frozen teacher, without an external verifier during distillation, and the reward equals vanilla OPD wherever the aggregate shift is zero. Across two Qwen model pairs and seven benchmarks, CC-OPD achieves the highest average among all evaluated student-training methods. A 1.5B student trained with CC-OPD surpasses its own 7B RL-trained teacher on the MulDimIF benchmark.
On-policy distillation transfers reasoning capabilities by training a student model on its own generated trajectories using token-level feedback from a teacher. However, we identify a critical bottleneck, \textbf{Supervision Fidelity Decay (SFD)}: as student-generated prefixes lengthen, the teacher's next-token distribution becomes less confident and less discriminative. Consequently, the teacher-dependent corrective signal in reverse-KL distillation weakens, causing student drift to compound across long reasoning chains. To mitigate SFD, we introduce \textbf{Lookahead Group Reward (\ours{})}. Building on the insight that next-step teacher confidence reflects the discriminative strength of future reverse-KL supervision, \ours{} evaluates the student's top-K candidate tokens by the teacher confidence they induce at the subsequent step and assigns a group-normalized reward. To maintain computational efficiency, we further design an entropy-triggered tree-attention mechanism. Across six math and code benchmarks, \ours{} improves mean@8 by \textbf{2.57} points over OPD for a 7B student, with gains increasing in longer-generation and reaching +\textbf{4.92} points on AIME-26 at 39k tokens.
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 +3
On-policy distillation (OPD) supervises a student language model on trajectories sampled from its current policy, but assigns equal credit to response tokens with unequal supervision value. Selective OPD addresses this limitation by allocating supervision non-uniformly across response tokens according to their estimated training value. Most existing criteria, however, focus primarily on optimization need, such as uncertainty or teacher-student disagreement, while task relevance, namely whether the supervision is tied to the semantic content of the current input, remains less directly characterized as a complementary dimension. To address this gap, we introduce Counterfactual Relevance for On-Policy Distillation (CROP), which operationalizes task relevance through a paraphrase-calibrated counterfactual sensitivity margin. For each source prompt, CROP constructs a validated original-paraphrase-counterfactual triplet, holds the student rollout fixed, and measures each response position by its sensitivity to a task-relevant condition change calibrated by its sensitivity to a meaning-preserving rewrite. Matched selection controls show that CROP identifies more useful supervision positions than random or lowest-relevance selection, while component comparisons confirm the value of both counterfactual sensitivity and paraphrase calibration. Across two teacher-student settings, CROP improves aggregate performance by 1.92 and 2.96 points over the strongest non-CROP selector. These results support task relevance as a complementary criterion for selective OPD and establish CROP as a model-internal, contrast-specific method for allocating token-level supervision.