Noisy expert imitation learning requires exponential samples for offline methods but polynomial for a variant of on-policy distillation under a noise condition.
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Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes
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On-policy distillation (OPD) is increasingly used in LLM post-training because it can leverage a teacher model to provide dense supervision on student rollouts. The standard implementation, however, usually reduces distribution matching to a sampled-token log-ratio, which can make the learning signal fragile on long rollouts whose prefixes drift away from the teacher's typical support. We revisit this formulation from both theoretical and implementation perspectives. Theoretically, token-level OPD is biased relative to sequence-level reverse-KL minimization, but admits a substantially tighter worst-case variance bound; a controlled synthetic study further shows that stronger future-reward coupling increases gradient variance and destabilizes training. Empirically, we identify three failure modes of sampled-token OPD: imbalanced token-level supervision, unreliable teacher guidance on student-generated prefixes, and tokenizer or special-token mismatch. These findings motivate teacher top-K local support matching, a truncated reverse-KL objective that compares teacher and student distributions over a teacher-supported token set at each prefix, together with top-p rollout sampling and special-token masking. Across single-task reasoning and multi-task benchmarks spanning agentic and reasoning settings, this objective improves optimization stability and yields a +19.8% performance gain over standard sampled-token OPD baselines, providing a practical recipe for more stable on-policy distillation.
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2026 50representative citing papers
SC-GRPO improves RL with verifiable rewards by multiplying GRPO gradients with self-induced per-token KL divergence, outperforming GRPO by 8.1% and DAPO by 5.9% on math, code, and agent benchmarks.
ZPPO improves distillation to small vision-language models by using binary and negative candidate prompts plus a replay buffer for hard questions, outperforming standard distillation and GRPO on a 31-benchmark suite with largest gains at the 0.8B scale.
PowerOPD applies the Box-Cox power transformation to create natively bounded, sign-consistent rewards for on-policy distillation, delivering up to +6.37 Avg@8 gains over vanilla OPD on math reasoning benchmarks while cutting compute costs.
A stop-gradient consistency regularizer mitigates context-induced degradation in on-policy distillation, improving robustness across 12 configurations.
AR-OPD disentangles privileged supervision via anchored residual guidance to reduce hindsight leakage in on-policy distillation, reporting gains of 2.3 points over full privileged OPD and 7.9 over SFT on reasoning tasks.
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.
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.
OPHSD uses harness-augmented models as teachers to distill reasoning capabilities into base LLMs, yielding strong standalone performance on classification and math tasks.
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.
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.
PBSD derives a reward-reweighted teacher distribution as the analytic optimum of a reward-regularized objective, yielding better stability and performance than KL-based self-distillation on math reasoning and tool-use tasks.
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.
RLSD mixes self-distillation for token-level policy difference magnitudes with RLVR for reliable update directions from response correctness to reach higher convergence and better training stability.
RAPS-DA improves RAG robustness to heterogeneous knowledge conflicts by training regime-specific peer specialists with hard routing and a dual-layer token selector for focused supervision.
RLCSD contrasts teacher-student distributional gaps under correct versus wrong hints to suppress privilege-induced style drift and concentrate supervision on task tokens, outperforming GRPO and prior OPSD on Qwen3 and Olmo models.
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.
SocraticPO adds Socratic-style teacher guidance and reward decay to RL rollouts for LLMs, improving performance on scientific reasoning benchmarks over baselines.
Introduces Lookahead Group Reward to address Supervision Fidelity Decay in on-policy distillation, yielding gains of 2.57 mean@8 points on math and code benchmarks for a 7B model.
ADWIN adaptively selects training horizons in on-policy distillation via prefix alignment checks, cutting end-to-end cost by up to 4.1x while matching or exceeding full-rollout accuracy on math and code benchmarks.
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.
On-Policy Consistency Training (OPCT) improves LLM safety metrics over supervised fine-tuning while largely preserving capabilities across three model families.
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