Boyan Li, Bingsen Chen, Chenghao Yang +3cs.CL cs.AI cs.LG
Reinforcement learning with verifiable rewards (RLVR) and on-policy distillation (OPD) have emerged as two dominant methods for post-training reasoning LLMs. Prior work uses OPD's dense token-level supervision to complement the sparse RL reward, fusing the two signals within a single step: either as a \emph{weighted-additive combination} or a \emph{teacher-modulated rescaling} of the RL advantage. In this paper, we show that a simple two-stage scheme, OPD-then-RL, consistently outperforms pure OPD, pure RLVR, and all such joint baselines across logic and math reasoning benchmarks. Beyond the empirical results, we further provide a systematic understanding of this through pass@$k$ behavior, learning dynamics, and parameter updates, yielding a consistent explanation: OPD expands the student's coverage of teacher-supported solutions and RL sharpens within that support, while jointly optimizing the two signals causes them to interfere.To provide a practical recipe, we find that the OPD validation score is the key signal for when to switch to RL, and that OPD is a better cold start for RL than SFT. Together, our results establish OPD-then-RL as a simple yet strong way to combine the two methods, turning two entangled signals into complementary stages.
On-policy distillation (OPD) accelerates post-training by providing dense token-level supervision from a frozen teacher on the student's own rollouts. Vanilla OPD applies this supervision uniformly across prompts, without checking whether the teacher is reliable for each prompt. Because reverse KL is mode-seeking, a confidently wrong teacher can induce a strong yet misleading update. Distributional proxies, such as entropy or teacher-student likelihood agreement, measure uncertainty or agreement but do not directly verify outcome correctness. We introduce Teacher-Gated On-Policy Distillation (TGOPD), built on the principle that teacher reliability should be verified at the prompt level before dense supervision is admitted. TGOPD estimates reliability from a small set of verifier-scored teacher probes and routes each prompt exclusively to dense OPD when the reliability check passes or to verifier-grounded GRPO otherwise. Across 4B and 35B students in mathematics, code, and instruction following, TGOPD outperforms Vanilla OPD in all six single-domain settings and achieves higher seven-benchmark averages at both scales under multi-domain training. By using otherwise-idle teacher capacity for reliability estimation, TGOPD also reduces teacher-side compute waste in asynchronous OPD, increasing teacher-node GPU utilization from 9.8% to 78.9% in the measured 4B single-domain run.
Sampled-token on-policy distillation (OPD) efficiently transfers capabilities from teacher to student using student-generated tokens, requiring teacher probabilities only for sampled tokens. Yet it frequently suffers from diversity distillation failure: the student's pass@1 improves while its pass@$k$ plateaus, failing to inherit the teacher's diversity. To explain this, we introduce First-Order Local Entropy Influence, a signed first-order proxy that decouples each update's entropy effect into the teacher--student log-probability gap and the student's local probability structure, and empirically links entropy contraction to negative-influence positions. Motivated by this, we propose Influence-Directed Adaptive On-Policy Distillation (IDA-OPD): rather than relying on costly full-vocabulary Forward-KL objectives, it preserves entropy-expanding updates while replacing entropy-contracting ones with divergence-adaptive advantage shrinkage, using only the teacher's sampled-token log-probability. Experiments on reasoning-oriented distillation show IDA-OPD consistently improves pass@$k$, inheriting the teacher's diversity through distillation, matches the strongest teacher-informed methods at strictly lower cost, and broadly maintains vanilla OPD's pass@1, all without full-vocabulary teacher information.
Spiking neural networks (SNNs) offer a path to energy-efficient language modeling through sparse encoding and event-driven computation, but training capable spiking language models from scratch remains difficult. A practical alternative is ANN-to-SNN migration through knowledge distillation (KD), where a pretrained artificial neural network (ANN) teacher supervises an SNN student. Existing migration approaches distill on fixed corpus prefixes, whereas autoregressive inference conditions on self-generated prefixes, creating prefix-source mismatch. It manifests as output-policy mismatch with the ANN teacher and internal spiking-dynamics drift between self-generated and matched corpus prefixes. On-policy distillation (OPD) offers a natural way to mitigate both manifestations by continuing teacher supervision on self-generated prefixes. We evaluate a teacher-only full-KL variant, Vanilla OPD, via a controlled stress test and observe it may suffer from delayed rollout-feedback collapse. This result shows that on-policy coverage alone does not ensure stable adaptation. Motivated by these findings, we propose SpikeOPD, a stable on-policy distillation framework for autoregressive SNNs that learns from self-generated prefixes while maintaining rollout stability. It applies full-KL teacher correction to reduce output-policy mismatch, while matched-prefix policy anchoring constrains policy departure from the frozen reference SNN on the same prefixes. Layerwise spike regularization further limits firing-rate deviations during on-policy adaptation. Across three model scales, SpikeOPD improves average accuracy over the corresponding KD SNNs by 0.8, 1.7, and 2.9 points at 0.125B, 0.35B, and 1.3B, respectively, while preserving their sparse-compute profiles.
On-policy distillation (OPD) supervises a student on its own trajectories with token-level signals from a frozen teacher, yet how a sampled loss allocates updates across tokens remains poorly understood. We analyze the gradient of the per-token K2 estimator of reverse KL with respect to the student logits. The $\ell_1$ norm of this gradient factorizes into the absolute teacher--student log-probability gap and a student-side softmax factor that grows as the sampled token becomes less likely under the student. In our math-distillation runs, these per-token norms are highly non-uniform: low-student-probability tokens account for a disproportionate share of their sum and are also enriched in large teacher--student gaps. As a lightweight intervention suggested by this analysis, we study Surprise-aware Reweighting (SuRe), a detached, bounded weighting rule that further amplifies this existing allocation. Across two Qwen3 student scales, SuRe improves several math metrics over vanilla OPD and shows no clear degradation on the selected out-of-domain benchmarks. Our primary contribution is therefore a gradient-level characterization of reverse-KL OPD trained with the K2 estimator, with SuRe as one empirical instantiation.
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 (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.
On-policy distillation (OPD) has emerged as an effective paradigm for transferring knowledge between language models, where a student is trained to align its next-token distribution with the teacher's along its own trajectories. To provide dense supervision at tractable cost, many works minimize the reverse Kullback-Leibler (KL) divergence between the student and teacher's normalized distributions over the teacher's top-$k$ tokens. However, this normalized objective discards the information about tail probability: the total probability outside the teacher's top-$k$ tokens. As a result, the optimization can steadily increase the student's tail probability and entropy, empirically degrading downstream accuracy. To address this issue, we propose Tail-Aware Top-$k$ OPD (\textbf{TA-OPD}), a novel distillation method that restores the missing tail probability signal. In particular, TA-OPD minimizes the reverse KL divergence over the top-$k$ tokens plus a tail token that carries the tail probability. In effect, TA-OPD better aligns the student's next-token distribution with the teacher's, preventing the increase in tail probability and entropy caused by top-$k$ normalization. Extensive experiments demonstrate the superiority of TA-OPD, improving Avg@8 by up to 8.05 points on common benchmarks. Our code is available at https://github.com/HuipengHuang/TA-OPD.
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 $λ$ 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 $λ$ 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 $λ_{b,t}=1+γ_b q_t$ 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.
On-policy distillation (OPD) has emerged as a core component of modern LLM post-training pipelines, yet we reveal a failure mode: degenerate agreement, where students exploit repetitive loops to achieve near-perfect token agreement with the teacher despite globally flawed responses. We therefore shift our focus from agreement to teacher-student mismatch, and find that mismatch tokens can be mainly categorized into two types: student-excess tokens and student-deficit tokens. Student-excess tokens are generated by the student but assigned near-zero probability by the teacher; their log-ratio corrections grow unbounded and destabilize the update. Student-deficit tokens, in contrast, are preferred by the teacher but rarely sampled by the student; their absence blocks the transfer of the teacher's reasoning patterns. To tackle these mismatch directions, we propose TIDE (Token-level Independent Deficit-Excess correction), which applies bounded Hellinger shaping to suppress the most severe sampled excesses and an analytic teacher top-$K$ injection to restore deficient probability mass without requiring deficit tokens to be sampled. Across mathematical reasoning benchmarks with multiple Qwen3 teacher-student pairs, TIDE consistently outperforms standard OPD and recent token-selection and reward-shaping baselines. Moreover, the gains of TIDE are more pronounced under strong teacher-student mismatch, where it improves Avg@8 from 6.9% to 20.3%, reduces average response length by a factor of 3.6, and substantially reduces formatting failures. Code is available at https://github.com/yzc-666/TIDE
Long-horizon agents accumulate growing contexts during interaction, impairing performance and stability. Compact memory mitigates this problem by compressing and rewriting the history retained between model invocations. Learning what to retain typically relies on proximal policy optimization (PPO) with final task rewards, but sparse rewards provide little guidance for individual memory updates. This limitation motivates on-policy distillation (OPD), which supplies dense teacher supervision on student rollouts. For such supervision to be valid, the teacher must evaluate each sampled action under the same state in which it was generated. However, the context rewriting performed during memory compression can break this alignment. When sampled responses are retained and re-encoded for later invocations, flattening the interaction into a persistent history may cause the teacher to score the action under a state that the student never visited during rollout. The action therefore remains on-policy by provenance, but not necessarily by state. We therefore propose Memory-Aligned On-Policy Distillation (MemOPD). MemOPD records the inputs and sampled outputs of each model invocation, restores its original token positions and causal visibility, and packs the reconstructed invocations for efficient teacher scoring. The teacher provides full-vocabulary supervision at the sampled action positions, while PPO preserves the final task objective. Experiments verify state alignment across several context updates and show that it improves F1 by 7.0% over persistent-history teacher scoring in a matched control. Overall, MemOPD-3B improves F1 over PPO by up to 416.2%, while packing yields up to a 1.63x speedup in actor computation during training. The code for this work is publicly available at: https://github.com/TPssp/MemOPD.
On-policy distillation (OPD) trains a student on its own rollouts with token-level supervision from teacher models, but its effectiveness can depend strongly on the warm-up stage before OPD. In this paper, we demystify warm-up for OPD from both data and training perspectives. For data, we find that effective warm-up relies on teacher-compatible chain-of-thought supervision, and that even incorrect teacher rollouts can provide comparable benefits to correct ones. This suggests that warm-up primarily transfers a teacher-compatible thinking pattern rather than merely correct answers. For training, we show that low-rank adaptation (LoRA) with a near-saturation training duration better balances in-domain adaptation and out-of-distribution generalization than full-parameter SFT. Based on these findings, we propose Simple-OPD, a plug-and-play initialization method that warms up the student on teacher-generated CoT with LoRA before OPD. Experiments across diverse settings demonstrate the effectiveness and robustness of Simple-OPD.
On-policy distillation (OPD) has become an effective approach for consolidating multiple task-specialized image generation models into a single student. However, existing OPD methods optimize the student mainly to match the teacher's output velocity, making the teacher the upper limit of the optimization objective. While output-level supervision alone leaves the student's blockwise representation evolution underconstrained, which weakens the transfer of capabilities that must be progressively developed across layers. We propose STEP-OPD, an on-policy distillation framework for image generation that extends the student's learning target beyond the teacher and introduces explicit constraints on its internal representation evolution. Instead of treating the teacher as the final target, we use the velocity difference between each task-specific teacher and the shared base model as a direction for further learning and add a scaled version of this difference to the teacher velocity. In addition, we align the direction and magnitude of representation changes between the student and teacher, enabling the student to learn how representations are progressively transformed across network blocks. Experiments on compositional alignment, text rendering, and human preference show that our method consistently improves Standard OPD methods. In particular, it increases the GenEval score of DiffusionOPD from 0.927 to 0.961, while also improving OCR and all preference-based metrics. The resulting unified student surpasses the corresponding single-task teachers across all three capability groups, showing that output extrapolation enables beyond-teacher learning. And representation change alignment provides complementary guidance for the student's internal transformations.
On-Policy distillation (OPD) transfers teacher capabilities by supervising student-sampled trajectories with dense token-level teacher signals. Recent selective OPD methods improve this process by prioritizing signals that are confident, informative, or learnable. However, the assumptions overlook a fundamental failure mode of language models: their token-level judgments can be driven by input-agnostic language priors, formatting conventions, or stereotyped reasoning templates rather than task-specific evidence. We refer to such optimization-relevant but weakly input-grounded supervision as spurious signals in OPD, which may produce large gradients while contributing little task-improving direction. To mitigate this issue, we propose SA-OPD, a Spurious-Signal-Aware On-Policy Distillation framework that identifies and filters misleading token-level supervision based on input-groundedness and optimization impact. SA-OPD introduces a lightweight input-groundedness proxy estimating whether a token-level distillation signal truly depends on the input. It then filters only tokens that simultaneously exhibit low input-groundedness and extreme distillation divergence, thereby removing high-impact spurious updates and achieving fine-grained OPD optimization. Extensive experiments on both large language model (LLM) and vision-language model (VLM) settings demonstrate that SA-OPD consistently outperforms Vanilla OPD and competitive selective methods. These results establish input-groundedness as a key dimension for OPD supervision selection and offer a simple, effective strategy for mitigating spurious updates.
On-policy distillation (OPD) samples trajectories from the current student policy and minimizes token-level divergence between student and teacher next-token distributions at prefixes along those trajectories. This aligns the distillation states with the student's own generation distribution. However, it still assumes that the complete teacher distribution is an appropriate target across student capacities. In vision--language reasoning, teacher corrections can depend on visual distinctions that a compact student cannot represent. Our target-scaling study shows that, as the target approaches the complete teacher distribution, the student realizes less of the prescribed shift and obtains worse downstream performance. We therefore propose \emph{Fisher-Projected On-Policy Distillation} (FP-OPD), which distills only locally realizable teacher corrections. FP-OPD uses continuous visual perturbations to estimate the student's local visual tangent space and projects the centered teacher--student log-probability gap onto this space under the student's Fisher metric. The resulting capacity-aware target is optimized with full-vocabulary reverse KL on student trajectories, retaining the standard OPD framework. In 8B-to-2B distillation, FP-OPD improves all seven evaluated multimodal benchmarks. It raises the average score by 2.77 points over the pretrained student and by 1.60 points over standard OPD. These results demonstrate that locally realizable teacher corrections provide a more effective target for distilling compact vision--language models.
On-policy distillation (OPD) trains student models on their own rollouts to reduce exposure bias. However, in multi-turn agent scenarios, early student errors can lead a trajectory away from the teacher's familiar domain. Existing curriculum learning methods regulate how much teacher support is used according to training progress, but cannot determine when it is needed. In light of this, we propose DASH-OPD, Discrepancy-Aware Switching with Hysteresis for OPD, the first agentic OPD method that can switch executors adaptively and bidirectionally. On each turn, DASH-OPD calculates a mean log-probability ratio between the two executors over action tokens as their discrepancy. Student-to-teacher ratios on student turns form drift signals, while teacher-to-student ratios on teacher turns form recovery signals. These signals are normalized and accumulated over multiple turns into drift and recovery evidence. DASH-OPD switches executors when the evidence exceeds its corresponding switching threshold. This multi-turn accumulation makes the switching hysteretic, preventing high-frequency switches caused by transient fluctuations. Across WebShop, ALFWorld, and ScienceWorld at two student-model scales, DASH-OPD outperforms five baselines in all 14 task-performance comparisons while yielding the shortest trajectories in nine of ten turn-count comparisons, offering the strongest overall performance-efficiency trade-off. This paper is a work in progress. Code, training logs, and model checkpoints will be released later.
Large language model training in open-ended domains lacks verifiable rewards, making task preferences difficult to formalize as effective supervision. Contexts can convey such preferences, yet provide little additional supervision once distilled into the student, motivating contexts that evolve with student performance. However, directly using evolving contexts as in-training supervision results in an unstable distillation target and conflicting distributions, requiring mechanisms to stabilize target and downweight conflicts. In this paper, we analyze the effect of contexts through a decomposition of the reverse KL objective, revealing two findings: the student is distilled toward the geometric mean of context-conditioned teachers, and the objective contains a conflict term that measures conflicts among these teachers. Based on this decomposition, we propose Flux-OPD, an OPD paradigm that uses evolving contexts as in-training supervision to capture task preferences in open-ended domains. Flux-OPD treats the differences between context-conditioned and context-free teachers as contextual difference signals, injects them as contextual corrections into the context-free teacher anchor, and weights their correction strength using the conflict term as an indicator. Experiments on open-ended tasks show that Flux-OPD outperforms existing OPD paradigms, highlighting the potential to combine teacher supervision with evolving contexts.
While on-policy distillation (OPD) effectively addresses sparse rewards and exposure bias in large language model post-training, its extension to flow models remains underexplored. To this end, we propose Flow Continuous Trajectory Supervision (FlowCTS), which matches subsequent student and reference trajectories initialized from the same student-visited state. Using the integral relation between trajectories and velocity fields, we derive a temporally weighted velocity-matching upper bound and discretize it into practical objectives parameterized by the number of supervision steps. Under a multi-reference setup, single-state FlowCTS-OPD outperforms vanilla KL-based OPD with faster convergence. FlowCTS-OPD improves GenEval from 0.90 to 0.93, OCR from 0.90 to 0.92, and PickScore from 22.75 to 23.06, while outperforming a mixed-reward RL baseline across all target metrics. Further analysis reveals a clear temporal supervision mismatch in vanilla KL-based OPD arising from its auxiliary SDE transition kernels. Beyond on-policy setting,FlowCTS also consistently outperforms vanilla SFT , particularly on OCR, while increasing supervision steps exhibit a trade-off between richer trajectory information and greater optimization difficulty.
Hao Wang, Kun Yuan, Wenlin Zhong +4cs.LG cs.AI cs.CL
Open-weight language models from different families exhibit complementary capabilities, motivating their consolidation into a compact student through on-policy distillation (OPD). However, full-vocabulary OPD typically assumes a shared tokenizer, while existing cross-tokenizer methods may discard teacher probability mass or assign it to student tokens with unrelated content. We introduce Byte-Prefix Marginalization (BPM), which re-expresses the teacher's next-token distribution over the student vocabulary in a shared byte space. Specifically, BPM assigns each teacher token's probability to the longest student token whose byte representation is a prefix of the teacher token's bytes, aggregates mass mapped to the same student token, and places otherwise unmatched mass in an explicit residual category. This produces a vocabulary-complete, byte-aligned, and mass-preserving target for dense OPD. The target exactly recovers the teacher-induced byte-prefix marginal when the relevant prefix does not span multiple teacher tokens (a condition satisfied at more than 99% of training positions) and uses a mass-preserving, chain-factorized lower bound otherwise. Across Qwen3-32B, GLM-Z1-9B-0414, and MiniMax-M2.7 as teachers, BPM consistently outperforms current cross-tokenizer methods on six mathematics and programming benchmarks, improving six-benchmark avg@8 by 3.7-6.6 points over the strongest baselines.
Yijun Liang, Yunjie Tian, Yijiang Li +4cs.CV cs.AI
On-policy self-distillation (OPSD) is promising as it removes the external teacher required by on-policy distillation (OPD), yet it still needs asymmetric information between teacher and student to ensure that the self-teacher provides a stronger learning signal than the student. Existing methods create this asymmetry either through privileged answers or visual evidence. We ask whether both can be removed, yielding a simpler form of OPSD driven purely by input conditioning. For this purpose, we propose Visual Contrastive Self-Distillation, namely VCSD, which converts image-content removal into an on-policy self-distillation signal. At each student-generated response prefix, the EMA teacher produces two next-token distributions under the same prompt and prefix -- one conditioned on the original image and the other on a content-erased control. Their token-wise log-probability difference highlights candidates whose likelihood is specifically increased by the instance-level visual content. We use this contrast to sharpen the teacher's original-image distribution within its plausible support, and distill the resulting full-distribution target into the student. Using ViRL39K dataset, VCSD consistently outperforms matched OPSD across Qwen3-VL and Qwen3.5 models. For example, on Qwen3-VL, it improves the seven-benchmark aggregate from $62.27\% \rightarrow 67.04\%$ at 2B, $71.30\% \rightarrow 73.16\%$ at 4B, and $72.51\% \rightarrow 76.26\%$ at 8B. Furthermore, VCSD requires no external teacher, privileged answers, visual evidence signals, reasoning traces, or additional inference-time cost.
Large language models are increasingly trained as interactive agents for long-horizon tasks involving multi-turn interaction, tool use, and environment feedback. Outcome-based reinforcement learning (RL) provides a practical optimization paradigm, but its sparse trajectory-level rewards offer limited guidance on intermediate decisions, leaving a supervision gap between episode-level outcomes and token-level policy learning. We propose SEED (SElf-Evolving On-Policy Distillation), a self-evolving framework that converts completed on-policy trajectories into training-time hindsight skills and distills their behavioral effect back into the policy model. SEED first fine-tunes the policy to analyze completed trajectories and generate natural-language skills that capture reusable workflows, decisive observations, or failure-avoidance rules. During RL, the current policy both collects trajectories and serves as the analyzer that extracts hindsight skills from them. Policy updates therefore improve subsequent decision making and skill analysis together, allowing hindsight supervision to evolve with the policy. SEED then re-scores the sampled actions under ordinary and skill-augmented contexts, converting the skill-induced probability shift into a dense token-level on-policy distillation signal. This signal is jointly optimized with outcome-based RL, keeping the auxiliary supervision aligned with the current trajectory distribution. Extensive experiments on text-based and vision-based agentic tasks show that SEED consistently improves performance and sample efficiency, exhibiting robust generalization to unseen scenarios. Our code is available at https://github.com/jinyangwu/SEED.
Conventional language-model distillation often relies on fixed teacher-generated data, which may not cover the states encountered by an evolving student policy. On-policy distillation (OPD) instead collects teacher or evaluator supervision on student-generated rollouts. However, existing OPD methods differ substantially in supervision form, tokenizer compatibility, teacher access, and supervision granularity, leading to fragmented implementations that are difficult to reproduce and extend. We present \textsc{EasyOPD}, an on-policy distillation framework built on verl, a distributed reinforcement-learning framework for large language models. \textsc{EasyOPD} separates user-side configuration, method-specific supervision logic, and verl-based execution. Its method modules connect to the shared backend through extension boundaries for loss construction, rollout metadata, reward processing, tokenizer alignment, and teacher-side computation. We instantiate representative methods for three OPD settings -- cross-tokenizer OPD, on-policy self-distillation, and step-wise OPD. Experiments on reasoning, code-generation, scientific-knowledge, and tool-use benchmarks show that these implementations can be executed through the same verl-based backend while retaining their method-specific objectives and task-dependent performance profiles. We release \textsc{EasyOPD} with runnable YAML configurations, documentation, and an installable demonstration package and video.
On-policy distillation (OPD) trains a student policy by matching a stronger teacher on the student's own trajectories, offering a promising framework for language agent training. However, its application to long-horizon agentic tasks remains insufficiently explored. We identify two key inefficiencies in vanilla agent OPD: (1) full-horizon rollouts often waste wall-clock resources on tail turns that provide weak and noisy KL supervision, and (2) trajectory-level KL objectives concentrate most of the loss on shallow tokens, leaving deeper decision turns under-trained once initial behaviors are aligned. To address these challenges, we propose TurnOPD, a turn-level budgeting strategy for efficient on-policy distillation of long-horizon agents. TurnOPD consists of two budget controllers: adaptive rollout-depth budgeting, which uses probe-based turn statistics to determine rollout length, and progressive turn-normalized loss budgeting, which gradually shifts KL weighting from token-level to turn-balanced supervision. Experiments on ALFWorld, WebShop, and Multi-Hop Search with task-specialized teacher models show that TurnOPD achieves superior validation accuracy under equal wall-clock training budgets and advances the accuracy--time frontier beyond vanilla OPD.
Simran Kaur, Narutatsu Ri, Yinghui He +2cs.AI cs.LG
Self-distillation is a promising recipe for self-improvement in language models. In this setting, a model can serve as its own teacher when given privileged information, such as a solution to a math problem. This seems especially appealing for thinking models, which can use test-time reasoning to absorb the privileged information. Surprisingly, we show that privileged self-distillation degrades thinking models on long reasoning traces: across five Qwen3 and OLMo thinking models evaluated on AIME24, AIME25, and HMMT25, privileged-context distillation causes a relative drop of up to 17% in avg@16 accuracy. The degradation scales with the amount of privileged context withheld from the student and is most pronounced at long rollout budgets, where thinking models otherwise obtain their largest gains. This failure mode is not specific to self-distillation: on-policy distillation (OPD) improves thinking models, but privileged OPD reverses these gains. Our diagnostics link this failure mode to how privileged teacher context reshapes learning at high-entropy forking positions, where multiple continuations remain plausible and may lead to different reasoning paths. Privileged context lowers fork rates in thinking-model rollouts but not in instruction-model rollouts. This leads to an interesting dichotomy, where privileged context can help instruction-tuned models but hurts stronger thinking models. The effect is visible when the student begins a self-correction branch, where privileged OPD penalizes sampled reconsideration tokens that vanilla OPD supports. Thinking models trained with a privileged teacher produce fewer verification, backtracking, and hedging markers, even after length normalization. These findings indicate that self-distillation for strong thinking models requires attention to token-level signal, especially around correction and reasoning steps.
On-policy distillation (OPD) offers superior capacity transfer by supervising student-sampled trajectories with dense token-level signals. To furnish high-quality supervision sources and thereby elevate the performance frontier of distillation, an intuitive direction is to infuse privileged information to either teacher or student itself. However, this additional input induces a potential failure mode we dub privilege illusion: a pattern that conflates the transferable capability gap that students are meant to close, and the information asymmetry gap that can only be mimicked but never replicated. This issue is further amplified by the inherent non-uniformity of token-level supervision, where only a small subset of tokens carries pivotal capability-bearing signals. To this end, we propose DOPD, an advantage-aware dual distillation paradigm that dynamically routes token-level supervision between privileged teacher and privileged student policies based on their advantage gap and relative probabilities. Each token receives supervision of different strength, objective, and strategy from either teacher or student itself, which transfers credible capability while simultaneously receiving auxiliary signals, to alleviate privilege illusion. Extensive experiments on both large language model (LLM) and vision-language model (VLM) settings demonstrate that DOPD consistently outperforms Vanilla OPD and other counterparts. Further results on stability, robustness, continual learning, and out-of-distribution tasks validate its superiority.
On-policy distillation (OPD) has a property absent in offline distillation and RL: teacher supervision quality depends on student competence. Incoherent rollouts yield noisy gradients; already-mastered tokens yield redundant ones. This creates waste at three scales (tokens, training phases, and prompts) yet existing methods supervise uniformly. We introduce SEAD, which uses entropy as a unified probe of this competence-dependent degradation at three scales: (1) joint teacher-student entropy partitions tokens into zones receiving tailored divergences or zero gradient (approx. 50% skipped); (2) a cosine schedule anneals from forward to reverse KL as competence grows; (3) a competence-gated curriculum introduces prompts easy-to-hard. These components are symbiotically necessary: token selection requires coherent rollouts (curriculum), annealing requires monotonic improvement (also curriculum). On OLMo-3 (7B to 32B), SEAD achieves +4.8 avg accuracy over vanilla OPD across six math benchmarks, with ablations confirming super-additive interactions.
On-policy distillation (OPD) trains a student policy using teacher signals computed on trajectories sampled by the student itself. Recent work shows that sampled-token OPD can be fragile on long-horizon reasoning tasks and that local teacher-support matching is a simple and effective repair. This paper introduces blockwise policy-drift gating, a lightweight student-only old-current drift controller for OPD under rollout reuse. The method computes log-probability shifts between the behavior student and the current student on the sampled token path, aggregates these shifts over fixed blocks or spans, and uses the resulting detached, mean-normalized gates to reweight OPD position losses. It does not change teacher targets, teacher top-K supports, or the rollout policy. In a six-variant Qwen3 math reasoning benchmark with a uniform 200-step training budget for all trained variants, we use pass@8 as the primary problem-level solve-rate metric. Fixed 64-token block gating improves sampled-token OPD mean pass@8 from 0.4978 to 0.5160 across AIME24, AIME25, MATH500, and AMC23. On Teacher-TopK/LSM, Block64 gives the best four-benchmark mean pass@8 among trained students. The results identify local old-current policy drift as a practical control signal for reused OPD rollouts and motivate block-level gating as a simple default for improving solve-rate robustness.
On-policy distillation (OPD) improves student models by training them on trajectories induced by their own policy, making it a promising approach for mitigating exposure bias in agent training. However, most OPD studies focus on single-turn settings, while realistic LLM agents interact with environments over multiple turns. In this regime, early errors can alter future observations and compound across the trajectory, and standard dense token-level OPD becomes brittle, as it may over-penalize semantically valid alternatives, reinforce local degeneracies such as repeated actions, and propagate unreliable teacher supervision on off-distribution histories. We propose SAGE-OPD, a verifier-free selective intervention framework specifically designed for multi-turn OPD. Instead of applying teacher supervision uniformly across all turns, SAGE-OPD first observes environment feedback and uses teacher judgment to decide whether each student response should be skipped or intervened on. To further address compounding errors, SAGE-OPD weights token-level distillation by teacher confidence, reducing the influence of uncertain teacher distributions on corrupted or ambiguous histories. Finally, SAGE-OPD applies loss normalization to preserve the overall loss scale of standard OPD while retaining selective turn-level weighting. Experiments on agent tasks show that SAGE-OPD consistently improves over baselines, achieving up to a 13.3% relative improvement in ALFWorld unseen success rate over standard OPD. Ablation studies further demonstrate that turn-level intervention, teacher confidence weighting, and loss normalization provide complementary benefits. Our results suggest that effective multi-turn OPD should remain on-policy, but teacher supervision should be selectively allocated to turns where intervention is necessary and reliable.
Anhao Zhao, Junlong Tong, Yingqi Fan +3cs.LG cs.AI
Standard on-policy distillation (OPD) for large language models estimates the reverse-KL objective using student-sampled tokens, yielding an unbiased single-sample Monte Carlo estimator that avoids vocabulary-wide computation. However, we show that this estimator suffers from severe training pathologies in practice: sample inefficiency, unstable generation dynamics, and a substantial performance gap compared to exact full-vocabulary OPD. Reward-level diagnosis traces these pathologies to the log-ratio reward, which is unbounded by construction, producing extremely high-variance gradients concentrated at early positions and persisting throughout training; standard post-hoc scaling fail as they operate only after this distortion occurs. To solve this problem, we propose PowerOPD: a family of natively bounded, sign-consistent rewards from the Box-Cox power transformation, parameterized by alpha > 0, of which the log-ratio is the degenerate alpha -> 0 limit. Across six mathematical reasoning benchmarks and four Qwen3 teacher-student pairs, PowerOPD achieves benchmark-averaged Avg@8/Pass@8 gains of up to +6.37/+5.71 over vanilla OPD, +3.01/+3.54 over post-hoc stabilization, and +2.59/+8.90 over full-vocabulary OPD, while reducing wall-clock time by 59.2% and peak GPU memory by 23.1%. Larger alpha generally improves accuracy, consistently shortens responses, and keeps gradient norms more than 3,000x smaller than vanilla OPD.
On-policy distillation (OPD) provides dense token-level supervision by asking a teacher to score student-generated rollouts. However, when the student drifts into an unrecoverable prefix, the teacher may locally agree with the degraded state, producing low reverse KL but little corrective training signal. We identify this persistent regime as a low-KL agreement trap. Further analyses show that tokens during and after such traps produce less useful supervision signals. We propose KAT (KL Agreement Trap Termination), an online OPD termination rule that detects persistent low-KL agreement with a dynamic training-adaptive threshold. By filtering weak supervision from degenerate agreement, KAT improves avg@k accuracy by 2.66% and pass@k by 3.43% across four mathematical benchmarks, while reducing average rollout length by 59.73%.