Online IL overcomes an information-theoretic bottleneck that offline IL faces in non-realizable settings even at horizon 1, under a new structural characterization of reward-relative misspecification.
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Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe
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On-policy distillation (OPD) has become a core technique in the post-training of large language models, yet its training dynamics remain poorly understood. This paper provides a systematic investigation of OPD dynamics and mechanisms. We first identify that two conditions govern whether OPD succeeds or fails: (i) the student and teacher should share compatible thinking patterns; and (ii) even with consistent thinking patterns and higher scores, the teacher must offer genuinely new capabilities beyond what the student has seen during training. We validate these findings through weak-to-strong reverse distillation, showing that same-family 1.5B and 7B teachers are distributionally indistinguishable from the student's perspective. Probing into the token-level mechanism, we show that successful OPD is characterized by progressive alignment on high-probability tokens at student-visited states, a small shared token set that concentrates most of the probability mass (97%-99%). We further propose two practical strategies to recover failing OPD: off-policy cold start and teacher-aligned prompt selection. Finally, we show that OPD's apparent free lunch of dense token-level reward comes at a cost, raising the question of whether OPD can scale to long-horizon distillation.
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TRL extends tandem training to RLVR pipelines, matching GRPO solo reasoning on Qwen3-4B math tasks while improving handoff robustness, reducing distributional drift, and increasing CoT legibility for the junior.
d-OPSD reframes on-policy self-distillation for dLLMs via suffix conditioning from self-generated answers and step-level supervision, outperforming RLVR and SFT on reasoning benchmarks with ~10% of the optimization steps.
KAT detects persistent low-KL agreement traps in on-policy distillation via a dynamic threshold to filter weak supervision, improving avg@k by 2.66% and pass@k by 3.43% on four math benchmarks while shortening rollouts by 59.73%.
OPD updates occupy a relaxed off-principal regime and rapidly lock into a low-dimensional subspace that is functionally sufficient for its performance, distinct from SFT and RLVR trajectories.
OPRD performs distillation in hidden-state space on on-policy data for deterministic gradients and better math benchmark performance, plus OPRD-Bridge for cross-architecture transfer via low-rank projectors.
DistIL applies distributional DAgger with forward cross-entropy to achieve monotonic policy improvement and better Pass@N from rich feedback in RL for reasoning tasks.
OmniOPD replaces token-level logit matching in on-policy distillation with Monte Carlo chunk-level semantic verification and a peak-entropy scheduler.
Self-Policy Distillation extracts a capability subspace from model gradients on correctness tokens, projects KV activations into it for self-generation, and fine-tunes LLMs to achieve up to 13-16% gains over baselines without external signals.
Life-Harness evolves reusable interventions from training trajectories to enhance frozen LLM agents on unseen tasks across seven deterministic environments, yielding 88.5% average relative improvement in 116 of 126 model-environment settings.
Decoupling prefix source from token-level KL direction in autoregressive sequence KL yields four objectives unifying SFT, DAgger, offline RL and OPD, with KL mixing and entropy-gated curriculum improving math reasoning accuracy and shortening responses.
Distillation signals align better with ideal updates on incorrect student rollouts than correct ones, with optimal teacher context depending on student capacity and task.
On-policy distillation has an extrapolation cliff at closed-form lambda*(p,b,c) set by teacher modal probability, warm-start mass, and clip strength, past which training shifts from format-preserving to format-collapsing.
vOPD stabilizes on-policy distillation gradients by subtracting a closed-form per-token negative reverse KL baseline as a detached control variate, preserving unbiasedness while lowering variance and matching expensive full-vocabulary methods.
Rubric-based on-policy distillation allows training student models using only teacher responses by generating scoring rubrics from contrasts and using them for on-policy optimization, achieving superior performance and up to 10x better sample efficiency than logit-based approaches.
MAD-OPD recasts on-policy distillation teachers as a debating collective to supply better supervision, lifting agentic and code performance over single-teacher OPD across multiple model sizes.
GUI-SD introduces on-policy self-distillation with visually enriched privileged context and entropy-guided weighting, outperforming GRPO and naive OPSD on six GUI grounding benchmarks while improving training efficiency.
SEAD applies entropy-guided token selection, KL annealing, and easy-to-hard curriculum to on-policy distillation and reports +4.8 average accuracy gain over vanilla OPD on six math benchmarks with OLMo-3 models.
Position bias in on-policy distillation degrades later-token supervision; IW-OPD weights tokens by accumulated discrepancy, yielding faster convergence and up to 6.9 point gains on AIME-2025.
Z-Reward trains a 27B reasoning teacher VLM on score distributions via GDSO and distills it via RISD into a 9B student, reaching 89.6% and 88.6% human preference accuracy with 41.3% optimization gain over SFT baseline.
PTD-PO supplies step-wise token-distribution supervision to student policies via in-context privileged hints derived from spatial attention and intermediate reasoning, while keeping the student in an answer-free context and using Top-K Jensen-Shannon divergence for stable alignment.
ViCuR introduces recoverable visual cues as teacher privilege in multimodal on-policy distillation, yielding +1.19 to +1.24 average gains over answer-based baselines across seven benchmarks with Qwen3-VL students.
SafeSteer restricts reverse KL penalty to safety tokens selected via activation steering, achieving strong safety on seven benchmarks with minimal degradation on five capability benchmarks using only 100 harmful samples and no general data.
DASD improves math reasoning in LLMs by adaptively directing self-distillation based on per-token entropy to balance exploration and step accuracy, outperforming prior self-distillation and RLVR baselines on six benchmarks.
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The Extrapolation Cliff in On-Policy Distillation of Near-Deterministic Structured Outputs
On-policy distillation has an extrapolation cliff at closed-form lambda*(p,b,c) set by teacher modal probability, warm-start mass, and clip strength, past which training shifts from format-preserving to format-collapsing.