Daily Papers

On-policy self-distillation (OPSD) has become a popular recipe for post-training LLM agents. It supervises the agent model at the token level with a stronger teacher view of the same model, obtained by conditioning on privileged information (PI). In this work, we show that in multi-turn agents, this paradigm teaches the student to act with confidence but without the information behind it. The trained agent behaves as if it had privileged information it never observed, and its performance falls well short of plain RL, in the worst case below the untrained base model. Therefore, we propose Privileged Self-Practice (PSP), which keeps the PI and moves it from the loss to the sampler. When the student's rollouts on a task mostly fail, we inject a short per-task instruction written by an analyzer model, sample the task again with the instruction in context, and train on the result with an unchanged GRPO objective. The privileged information stays in the prompt and never enters the loss. Across AppWorld and SWE-bench Verified, with three different student models, PSP obtains the best average score in every setting and is the only method that consistently outperforms plain GRPO, improving task-goal completion by up to 65% on AppWorld and the resolved rate by up to 61% on SWE-bench Verified.

Building reliable robot capabilities across diverse tasks requires substantial human effort to develop and maintain skills, design rewards, and integrate perception with control. We present Reconstruct, Practice, Go Real (RPG), a framework for autonomous improvement of robot execution systems without updating model weights. RPG identifies manipulation capabilities in an offline dataset and constructs related practice tasks in simulation. During practice, RPG uses execution feedback, privileged simulator state, and available dataset videos to diagnose failures. It develops new reusable symbolic skills, refines existing skills, and revises the system prompt based on these diagnoses. Cross-task evaluation tests individual candidate changes and merged revisions before they are retained for reuse. At test time, a multimodal LLM uses the resulting system prompt and skill library to coordinate perception and robot control. On held-out initializations of 22 manipulation tasks, RPG improves task success from 28.6% after the first practice round to 95.0% after 15 rounds, outperforming all evaluated baselines, including ASPIRE (75.5%) and CaP-Agent0 powered by GPT-6 Astra Pro (60.0%). After a common calibration and hardware-adaptation procedure, the frozen system succeeds in all 30 physical trials, with ten trials on each of three tasks. Project Website: https://rpg-robot.github.io/

Whether AI models can introspect is an increasingly important practical question. But there is no consensus on how introspection is to be defined. Beginning from a recently proposed ''lightweight'' definition, we argue instead for a thicker one. According to our proposal, introspection in AI is any process which yields information about internal states through a process more reliable than one with equal or lower computational cost available to a third party. Using experiments where LLMs reason about their internal temperature parameters, we show they can appear to have lightweight introspection while failing to meaningfully introspect per our proposed definition.

Reinforcement learning (RL) has been widely used to train LLM agents for multi-turn interactive tasks, but its sample efficiency is severely limited by sparse rewards and long horizons. On-policy self-distillation (OPSD) alleviates this by providing dense token-level supervision from a privileged teacher that has access to ground-truth answers. However, such fixed privileged information cannot capture the diverse valid strategies in agent tasks, and naively combining OPSD with RL often leads to training collapse. To address these limitations, we introduce Skill-SD, a framework that turns the agent's own trajectories into dynamic training-only supervision. Completed trajectories are summarized into compact natural language skills that describe successful behaviors, mistakes, and workflows. These skills serve as dynamic privileged information conditioning only the teacher, while the student always acts under the plain task prompt and learns to internalize the guidance through distillation. To stabilize the training, we derive an importance-weighted reverse-KL loss to provide gradient-correct token-level distillation, and dynamically synchronize the teacher with the improving student. Experimental results on agentic benchmarks demonstrate that Skill-SD substantially outperforms the standard RL baseline, improving both vanilla GRPO (+14.0%/+10.9% on AppWorld/Sokoban) and vanilla OPD (+42.1%/+40.6%). Project page: https://k1xe.github.io/skill-sd/

Deep search agents have emerged as a promising paradigm for addressing complex information-seeking tasks, but their training remains challenging due to sparse rewards, weak credit assignment, and limited labeled data. Self-play offers a scalable route to reduce data dependence, but conventional self-play optimizes students only through sparse outcome rewards, leading to low learning efficiency. In this work, we observe that self-play naturally produces a question construction path (QCP) during task generation, an intermediate artifact that captures the reverse solution process. This reveals a new source of privileged information: self-play can provide high-quality privileged information for the self-distillation at low cost and at scale, without relying on human feedback or curated privileged information. Leveraging this insight, we propose Privileged Information Self-Play (π-Play), a novel multi-agent self-evolution framework combining self-play and self-distillation. In π-Play, an examiner generates tasks together with QCPs, and a teacher employs QCP as privileged context to densely supervise a student via self-distillation. This design transforms sparse-reward self-play into a dense-feedback co-evolution. Extensive experiments show that data-free π-Play surpasses fully supervised search agents and improves evolutionary efficiency by 2-3times over conventional self-play. Code is available at https://github.com/zhyaoch/pi-play.

Enabling agents to learn from experience and internalize it into their policy has become a central problem in self-evolving AI. On-policy self-distillation (OPSD) offers an effective pathway by using a privileged self-teacher to provide dense supervision on the student's own trajectories; however, existing methods still rely heavily on designer-specified privileged artifacts (e.g., answers, feedback, skills, or trajectories), limiting the end-to-end learnability and scalability required for continual self-improvement. In this work, we introduce Latent On-Policy Self-Distillation (LOPD), which, rather than proposing another hand-crafted OPSD variant with a newly prescribed form of privileged context, makes the teacher's privileged context itself learnable end-to-end from experience. Technically, LOPD retrieves relevant experiences and composes them into continuous latent tokens that condition a self-teacher, while the student generates trajectories from the task and interaction history and receives dense token-level supervision at every visited prefix. We further introduce a privileged-margin objective to stabilize and regulate the learning of latent context. Empirically, LOPD demonstrates (I) strong performance, outperforming RLVR and representative OPSD methods including OPSD, SDPO, and Skill-SD across both agentic tool use and code generation; and (II) high learning efficiency, surpassing GRPO and Skill-SD with less than 30% of their rollout budget. Ablation studies further provide direct evidence that making privileged context learnable is necessary for realizing these gains. Together, these results position LOPD as a step toward a more scalable and self-directed paradigm for agent evolution.

On-policy self-distillation (OPSD) trains a large language model using supervision from a teacher instantiated from the same model as the student. The teacher is conditioned on privileged information (PI), such as verified solutions. The student, which does not observe PI, learns from the teacher's next-token distributions along its own sampled responses. However, PI can bias supervision toward shortcut reasoning with limited verification or reconsideration, accompanied by a sharp drop in the entropy of the output distribution. To address this challenge, we introduce self-distillation with verbal regularization (VRSD), which uses system prompts to regulate how the teacher uses PI, thereby encouraging rethinking and exploration to counteract premature commitment. Theoretically, we model prompting as attenuating the influence of PI on the teacher distribution and derive conditions for entropy preservation. Across three models and four tasks, VRSD improves Pass@1 over OPSD in 11 of 12 model-task settings, by 3.9 percentage points on average, while generally maintaining higher token entropy.

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.

Multi-turn agents trained with reinforcement learning (RL) receive a single scalar reward per trajectory, which motivates self on-policy distillation (OPD) to supply dense token-level supervision from a self-teacher with privileged task skills, letting a skill-free student internalize them. This recipe, however, is undermined by two findings in agentic tasks: privileged information alone does not always make a teacher reliable, and the benefit of teacher supervision is stage-dependent. We therefore propose RetireOPD (Self-Retiring On-Policy Distillation), which first optimizes a decoupled, skill-conditioned teacher with environment rewards and then trains a skill-free student jointly with RL and OPD. Rather than following a predefined distillation schedule, RetireOPD adopts Adaptive Retirement: the student drops the teacher on its own once their discrepancy stops shrinking and it reaches a target fraction of the teacher's success rate, after which training proceeds with RL alone. Across Qwen2.5 models from 1.5B to 7B, RetireOPD improves ALFWorld success rate over RL baseline by 14.1% to 18.8% and WebShop accuracy by 11.8% to 19.0%, and surpasses its own skill-conditioned teacher in every setting.

On-policy (self) distillation (OPSD) is increasingly adopted for language-model post-training. It strengthens the teacher with privileged information but can induce a privilege illusion: the student learns privilege-dependent behavior it cannot reproduce from its inference-time context, yet behaves as if the training-time privileged information remained available, ultimately degrading performance. In this paper, we identify information asymmetry between the privileged teacher and the student at inference as the root cause of this failure in OPSD. To resolve this asymmetry, we propose Dual-Anchored Policy Distillation (DAPD), a unified framework with two levels of anchoring. Dual-Path Anchoring (DPA) introduces a self-conditioned bridge and aligns reference and rollout behavior along two matched-information paths, preventing privilege-dependent behavior from being transferred to the inference-time student. Dual-Source Anchoring (DSA) applies these paths in both reference-to-rollout and rollout-to-reference directions, reducing reliance on privileged reference guidance while preserving correctness supervision. Extensive experiments show that DAPD significantly alleviates privilege illusion, outperforming OPSD on Qwen3-4B by +2.00 points on average across tasks. Notably, its gains persist across scales, reaching +2.69 at 4B and +2.78 at 32B.

On-policy self-distillation (OPSD) uses a privileged teacher to supervise a reasoning model on prefixes sampled from its own rollouts. Yet each rollout also reveals how the student's response unfolds and whether it succeeds, student-specific hindsight that standard OPSD does not use to form the teacher. We introduce Privileged Adaptation from Student Trajectories (PAST), which treats each completed student trajectory as additional privileged information for the OPSD teacher while leaving the student's distillation prefixes unchanged. PAST preserves the student's next-token distribution on correct trajectories and uses failed trajectories to adapt the teacher toward verified success under student-proximity regularization. We characterize what such a trajectory-conditioned teacher can transfer to a prefix-only student. Forward-KL distillation projects the teacher distributions to their conditional arithmetic mean given the prefix. This projection separates trajectory-specific variation that remains privileged from the mean policy shift available to the student. For correct trajectories, the unclipped population objective also has the frozen student as an ideal distributional fixed point. Across three mathematical reasoning benchmarks, PAST improves the Avg@12 macro average over Vanilla OPSD by 5.6 percentage points. A 2times2 factorial study shows gains from both complete-trajectory access and teacher adaptation, while trajectory removal and shuffling confirm that the adapted teacher uses the matching hindsight context.

Language-model agents are usually trained by reinforcement learning from one reward per episode, and privileged self-distillation enriches it by letting the same policy, given a skill, teach its skill-free self through token probabilities. However, we identify two phenomena that question this channel. Invisible Advantage: a skill in context lifts WebShop success from 42.2% to 56.2%, yet changes the probabilities of fewer than a quarter of the sampled tokens. Much to Align: a skill changes the hidden states of over 80% of response tokens, in a way that linear probes can trace back to the specific skill. To exploit this, we propose Privileged Representation On-policy Self-Distillation (PR-OPD). After a GRPO warm start, the policy writes a hindsight skill for each trajectory, re-reads its own responses with that skill as a stop-gradient teacher, and aligns its projected hidden states to the teacher's at every layer alongside the reward objective, with no external skill library, separate teacher, or inference overhead. On ALFWorld and WebShop with two backbones, PR-OPD achieves the best overall results in every setting, improving over GRPO by up to 4.7 points in ALFWorld success and 14.0 points in WebShop accuracy. Code is available at https://github.com/balibata/PR-OPD.

Skill memories can improve agentic reinforcement learning by reusing past experience as textual guidance, but retrieved skills are not oracular: they may help in one state while misleading the same policy in another. This makes the common privileged-teacher assumption fragile, namely that a skill-conditioned prompt can be treated as a fixed teacher for the no-skill prompt. We introduce UCOB, a framework for learning to utilize and evolve agentic skills via credit-aware on-policy bidirectional self-distillation. UCOB treats skill-conditioned and no-skill prompts as two on-policy context views of the same model, compares their return-to-go within the same task and anchor state, and uses the higher-return view as the local teacher. This local credit signal internalizes useful skill-conditioned behavior, corrects misleading skill usage, and guides task/state skill memory updates, utility-aware retrieval, and reflection self-training. Experiments on agentic tasks, including ALFWorld, WebShop, and Search-QA, show that UCOB outperforms skill-free RL, skill-memory baselines, and self-distillation methods across model scales, with up to 23.5 and 18.0 point gains over SOTA baselines on ALFWorld and WebShop. Ablations and analyses further validate its core mechanisms, continual adaptation across environments, and modest training overhead. Code is available at https://github.com/TU2021/UCOB.

Long-horizon contact-rich tasks are challenging to learn with reinforcement learning, due to ineffective exploration of high-dimensional state spaces with sparse rewards. The learning process often gets stuck in local optimum and demands task-specific reward fine-tuning for complex scenarios. In this work, we propose a structured framework that leverages privileged actions with curriculum learning, enabling the policy to efficiently acquire long-horizon skills without relying on extensive reward engineering or reference trajectories. Specifically, we use privileged actions in simulation with a general training procedure that would be infeasible to implement in real-world scenarios. These privileges include relaxed constraints and virtual forces that enhance interaction and exploration with objects. Our results successfully achieve complex multi-stage long-horizon tasks that naturally combine non-prehensile manipulation with grasping to lift objects from non-graspable poses. We demonstrate generality by maintaining a parsimonious reward structure and showing convergence to diverse and robust behaviors across various environments. Additionally, real-world experiments further confirm that the skills acquired using our approach are transferable to real-world environments, exhibiting robust and intricate performance. Our approach outperforms state-of-the-art methods in these tasks, converging to solutions where others fail.

On-policy self-distillation (OPSD) combines student generated trajectories with dense supervision from a privileged teacher of the same model. Its pointwise clipping protects the student from locally incompatible teacher directions, but the fixed teacher receives no feedback about the supervision the student rejects, which limits effective learning from the teacher. We introduce DualOPSD, which alternates updates in a coupled teacher-student system. The student retains OPSD's clipped forward KL objective. The privileged teacher adapts to the updated student after each student step. A residual target based on the frozen initial model preserves the effect of privileged context during teacher adaptation. Across Qwen3-8B/4B/1.7B and three math benchmarks, DualOPSD improves avg@12 accuracy over OPSD by 9.83 percentage points. Further diagnostic analyses show lower bidirectional KL, less persistent mismatch, and retained sensitivity to privileged reference. Together, these results demonstrate that DualOPSD can be a more effective form of privileged self-distillation. Code is available at: https://github.com/on1262/DualOPSD.

On-policy distillation trains a language model on its own generations while a teacher scores them token by token. It combines the dense supervision of imitation learning with the on-policy sampling of reinforcement learning. But it requires a second, larger model to act as teacher. On-Policy Self-Distillation (OPSD) removes that cost. The teacher is the model itself, conditioned on privileged information the student will not have at test time, such as a reference solution, a plan, or environment feedback. The teacher is no stronger than the student, only better informed. Early results were promising, with accuracy comparable to reinforcement learning at a fraction of the generated tokens. But the same asymmetry that produces the signal also biases it. One failure mode now dominates the field: collapse, the progressive narrowing of the set of reasoning paths the model can produce. Collapse is not specific to OPSD, though privileged information aggravates it. This review treats collapse as a symptom governed by three levers: (i) where the signal is applied, that is, how tokens are weighted; (ii) what the teacher is shown, that is, the nature of the privileged information; and (iii) when the signal changes, that is, the teacher's dynamics and the decay of guidance. We restrict our scope to mathematical reasoning, where the method originated and where its failure modes are best documented. We report no new experiments. The contribution is structural: a shared vocabulary for phenomena named differently across papers, and a clear line between what is settled and what is still disputed.

On-policy self-distillation has recently emerged as an effective approach for improving language-model reasoning by supervising students with a frozen or EMA version of themselves that receives privileged information. Its application to multimodal large language models (MLLMs), however, remains largely unexplored. Recent approaches use privileged visual information, such as image crops corresponding to a question, to improve fine-grained perception, but their gains are confined to tasks that benefit from such visual zooming and require either human-annotated grounding data or external teacher models. We introduce a different form of on-policy self-distillation for MLLMs that provides the teacher with textual, spatially grounded guidance identifying the visual elements relevant to a query. We use procedurally generated scenes with automatically available object identities and spatial coordinates, enabling scalable and annotation-free post-training. The teacher uses this spatial guidance to locate and integrate evidence from multiple relevant image regions, while the student learns to reproduce the resulting behavior from the image and question alone. Our approach consistently improves performance on counting, document and chart understanding benchmarks across multiple models. Importantly, although post-training uses only synthetic scenes, the resulting improvements transfer to real-world perception benchmarks, yielding a 3.23-point gain in average performance across CVBench, V*, ZoomBench, BLINK, HR-Bench, and MME-RealWorld. These results show that spatially grounded privileged information can induce broader perceptual capabilities through on-policy self-distillation, enabling substantial synthetic-to-real transfer beyond the task and data distribution used for post-training. Project page: https://github.com/sirkosophia/Where-OPD

Training-time privileged information (PI) can enable language models to succeed on tasks they would otherwise fail, making it a powerful tool for reinforcement learning in hard, long-horizon settings. However, transferring capabilities learned with PI to policies that must act without it at inference time remains a fundamental challenge. We study this problem in the context of distilling frontier models for multi-turn agentic environments, where closed-source systems typically hide their internal reasoning and expose only action trajectories. This breaks standard distillation pipelines, since successful behavior is observable but the reasoning process is not. For this, we introduce π-Distill, a joint teacher-student objective that trains a PI-conditioned teacher and an unconditioned student simultaneously using the same model. Additionally, we also introduce On-Policy Self-Distillation (OPSD), an alternative approach that trains using Reinforcement Learning (RL) with a reverse KL-penalty between the student and the PI-conditioned teacher. We show that both of these algorithms effectively distill frontier agents using action-only PI. Specifically we find that π-Distill and in some cases OPSD, outperform industry standard practices (Supervised finetuning followed by RL) that assume access to full Chain-of-Thought supervision across multiple agentic benchmarks, models, and forms of PI. We complement our results with extensive analysis that characterizes the factors enabling effective learning with PI, focusing primarily on π-Distill and characterizing when OPSD is competitive.

Long-horizon agentic tasks pose a fundamental credit assignment challenge for outcome-base reinforcement learning: trajectory-level rewards verify final correctness but provide limited guidance on which intermediate reasoning steps or tool interactions contribute to the outcome. The difficulty is especially pronounced in multi-turn search agents, where successful trajectories may contain misleading actions and failed trajectories may contain valuable evidence-gathering steps. We propose PBSD (Privileged Bayesian Self-Distillation), a Bayes-calibrated self-distillation method for fine-grained credit assignment under sparse final rewards. PBSD measures trajectory quality through the posterior-to-prior probability ratio of the verified answer and applies Bayes' rule to convert this hard-to-estimate answer-side ratio into a tractable likelihood ratio between a standard student model and a privileged answer-conditioned teacher model. Autoregressive decomposition of this Bayesian evidence score yields turn-level signals that identify whether each intermediate turn supports or undermines the verified outcome. Consequently, PBSD provides a principled and elegant reweighting scheme that transforms sparse outcome supervision into Bayes-calibrated turn-level credit signals, while remaining fully compatible with standard policy optimization. Experiments demonstrate that PBSD consistently enhances performance across both in-domain and out-of-domain settings, and effectively transfers knowledge from short-context training to long-context inference, suggesting that its fine-grained credit assignment mechanism facilitates more effective policy learning and yields improved generalization.

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 Self-Distillation (OPSD) is commonly interpreted as the transfer of privileged information: a teacher observes the verified solution to the target problem and supervises the student's trajectory. However, this interpretation conflates two effects. The reference solution not only reveals the answer to the current instance but also changes the context under which the teacher provides token-level supervision. We investigate the role of target-specific privilege with OP^{2}SD (On-Policy Self-Distillation from Other Problems), which replaces the paired reference with a problem and solution from a different example, while preserving the student rollout, teacher, and distillation objective. Across three models and three mathematics benchmarks, OP^{2}SD improves over the base model, remains competitive with OPSD. The success of OP^{2}SD implies that OPSD gains do not necessarily come from access to the reference solution, and that the teacher's context-induced behavior is an important factor.

Aerial grasp-and-lift tasks require whole-body coordination across approach, acquisition, and lifting under partial target observations. Early approach failures can limit exposure to later task stages during training, while changing visibility complicates alignment and closure timing during execution. We present a recurrent teacher-student framework that learns a single policy in simulation to jointly command flight, arm motion, and gripper closure without an explicit task-phase input. A privileged teacher learns through reinforcement learning with a critical-state curriculum that exposes acquisition and lifting states before connecting them to normal approach trajectories. Its behavior is distilled into a recurrent visual student that replaces privileged target states with dual-view point clouds and proprioception, integrating observation history for closed-loop control. A dedicated closure objective supervises closure timing from sustained model-defined readiness sequences. Training and primary evaluation use a simulated acquisition-and-payload model with condition-triggered latching, virtual attachment, and wrench-based payload loading for short-distance lifting. Across 8,996 completed simulation episodes under this model, the frozen student achieves full-task success rates of 99.97%, 97.14%, and 95.84% under nominal, physics/control-randomized, and additional camera-randomized conditions, respectively. The nominal latch-count-weighted mean of per-seed 90th-percentile alignment errors at acquisition is 8.12 mm.

While large language models (LLMs) show impressive decision-making abilities, current methods lack a mechanism for automatic self-improvement from errors during task execution. We propose LEAP, an iterative fine-tuning framework that continually improves LLM agents using feedback from AI expert teachers. Our key insight is to equip the expert teachers with a privileged state -- information that is available during training but hidden at test time. This allows even weak experts to provide precise guidance, significantly improving the student agent's performance without access to privileged information at test time. We evaluate LEAP on diverse decision-making benchmarks, including text-based games (ALFWorld), web navigation (WebShop), and interactive coding (Intercode Bash). Our experiments show that LEAP (1) outperforms behavior cloning and ReAct baselines (2) enables weak student models (e.g., Llama3-8B) to exceed the performance of strong teacher models (GPT4-o), and (3) allows weak models to self-improve using privileged versions of themselves. We also provide a theoretical analysis showing that LEAP's success hinges on balancing privileged information with the student's realizability, which we empirically validate. Our code is available at https://leap-llm.github.io

Knowledge distillation improves large language model (LLM) reasoning by compressing the knowledge of a teacher LLM to train smaller LLMs. On-policy distillation advances this approach by having the student sample its own trajectories while a teacher LLM provides dense token-level supervision, addressing the distribution mismatch between training and inference in off-policy distillation methods. However, on-policy distillation typically requires a separate, often larger, teacher LLM and does not explicitly leverage ground-truth solutions available in reasoning datasets. Inspired by the intuition that a sufficiently capable LLM can rationalize external privileged reasoning traces and teach its weaker self (i.e., the version without access to privileged information), we introduce On-Policy Self-Distillation (OPSD), a framework where a single model acts as both teacher and student by conditioning on different contexts. The teacher policy conditions on privileged information (e.g., verified reasoning traces) while the student policy sees only the question; training minimizes the per-token divergence between these distributions over the student's own rollouts. We demonstrate the efficacy of our method on multiple mathematical reasoning benchmarks, achieving 4-8x token efficiency compared to reinforcement learning methods such as GRPO and superior performance over off-policy distillation methods.

Reinforcement Learning (RL) has recently achieved remarkable success in robotic control. However, most works in RL operate in simulated environments where privileged knowledge (e.g., dynamics, surroundings, terrains) is readily available. Conversely, in real-world scenarios, robot agents usually rely solely on local states (e.g., proprioceptive feedback of robot joints) to select actions, leading to a significant sim-to-real gap. Existing methods address this gap by either gradually reducing the reliance on privileged knowledge or performing a two-stage policy imitation. However, we argue that these methods are limited in their ability to fully leverage the available privileged knowledge, resulting in suboptimal performance. In this paper, we formulate the sim-to-real gap as an information bottleneck problem and therefore propose a novel privileged knowledge distillation method called the Historical Information Bottleneck (HIB). In particular, HIB learns a privileged knowledge representation from historical trajectories by capturing the underlying changeable dynamic information. Theoretical analysis shows that the learned privileged knowledge representation helps reduce the value discrepancy between the oracle and learned policies. Empirical experiments on both simulated and real-world tasks demonstrate that HIB yields improved generalizability compared to previous methods. Videos of real-world experiments are available at https://sites.google.com/view/history-ib .

Agentic reinforcement learning enables LLM agents to learn through interaction, but sparse trajectory-level rewards reveal success without identifying which intermediate decisions deserve credit. Training-only privileged skills can provide denser supervision by allowing the same frozen policy snapshot to rescore fixed tokens from skill-free trajectories while conditioned on task-matched procedural skills. Existing methods, however, do not jointly calibrate teacher scores across interaction steps, relate teacher confidence to realized returns, and integrate the resulting signal into native reward-to-advantage construction. We introduce Agentic Reinforcement Learning with Self-Distilled Reward Shaping (ADRS), a framework for constructing return-associated token-level credit for multi-turn language agents. ADRS centers and normalizes privileged token scores within each step, modulates them with a return-associated Teacher Value Advantage (TVA) gate based on within-group confidence--return association, and incorporates the gated token signal into native RL credit construction. Together, these components determine what the teacher prefers, when that preference is return-relevant, and how it enters the native reinforcement-learning credit path, while keeping rollouts and inference skill-free. Finally, experiments across three interactive benchmarks show that ADRS consistently improves performance on long-horizon tasks, with gains persisting across RL backbones, reduced-data settings, unseen tasks, and extended training. For anonymous review, our code is available at the following the link: https://github.com/gitrxh/ADRS-arxiv

Humans use introspection to evaluate their understanding through private internal states inaccessible to external observers. We investigate whether large language models possess similar privileged knowledge about answer correctness, information unavailable through external observation. We train correctness classifiers on question representations from both a model's own hidden states and external models, testing whether self-representations provide a performance advantage. On standard evaluation, we find no advantage: self-probes perform comparably to peer-model probes. We hypothesize this is due to high inter-model agreement of answer correctness. To isolate genuine privileged knowledge, we evaluate on disagreement subsets, where models produce conflicting predictions. Here, we discover domain-specific privileged knowledge: self-representations consistently outperform peer representations in factual knowledge tasks, but show no advantage in math reasoning. We further localize this domain asymmetry across model layers, finding that the factual advantage emerges progressively from early-to-mid layers onward, consistent with model-specific memory retrieval, while math reasoning shows no consistent advantage at any depth.

Humans acquire knowledge by observing the external world, but also by introspection. Introspection gives a person privileged access to their current state of mind (e.g., thoughts and feelings) that is not accessible to external observers. Can LLMs introspect? We define introspection as acquiring knowledge that is not contained in or derived from training data but instead originates from internal states. Such a capability could enhance model interpretability. Instead of painstakingly analyzing a model's internal workings, we could simply ask the model about its beliefs, world models, and goals. More speculatively, an introspective model might self-report on whether it possesses certain internal states such as subjective feelings or desires and this could inform us about the moral status of these states. Such self-reports would not be entirely dictated by the model's training data. We study introspection by finetuning LLMs to predict properties of their own behavior in hypothetical scenarios. For example, "Given the input P, would your output favor the short- or long-term option?" If a model M1 can introspect, it should outperform a different model M2 in predicting M1's behavior even if M2 is trained on M1's ground-truth behavior. The idea is that M1 has privileged access to its own behavioral tendencies, and this enables it to predict itself better than M2 (even if M2 is generally stronger). In experiments with GPT-4, GPT-4o, and Llama-3 models (each finetuned to predict itself), we find that the model M1 outperforms M2 in predicting itself, providing evidence for introspection. Notably, M1 continues to predict its behavior accurately even after we intentionally modify its ground-truth behavior. However, while we successfully elicit introspection on simple tasks, we are unsuccessful on more complex tasks or those requiring out-of-distribution generalization.

On-policy self-distillation provides dense supervision for reasoning models via a privileged self-teacher. However, this supervision reflects local token preferences rather than the expected return of an unguided student continuation. Recent methods combine this signal with GRPO. They use GRPO for update directions and the teacher for signal scaling. However, we demonstrate a more effective integration within PPO. Specifically, we identify complementary positional dynamics: privileged information enhances a critic's value-prediction accuracy toward the response's end, whereas self-teacher guidance is strong initially, drops mid-generation, and rebounds finally. These insights motivate Value-Augmented Self-Distillation Policy Optimization (VASPO), wherein a self-teacher and critic evaluate identical privileged information at student-generated prefixes. The critic computes token-level PPO advantages from predicted continuation returns, while the self-teacher modulates selected positive advantages via bounded probability ratios. Across six mathematical reasoning benchmarks, VASPO improves mean accuracy over PPO by 2.59 and 1.81 percentage points on Qwen3-4B and OLMo3-7B variants, respectively, and achieves the highest mean accuracy among evaluated methods on Knights and Knaves. Our code is available at https://github.com/cii030/VASPO.

On-policy distillation (OPD) improves reasoning models by learning the token-level discrepancy between a stronger teacher and an on-policy student. However, this discrepancy does not purely reflect the capability gap between the teacher and the student: it also contains deviations arising from the teacher itself, which are consequently mixed into the observed teacher--student discrepancy and indiscriminately learned by standard OPD during training. This issue is further exacerbated by privileged OPD, where privileged information induces larger teacher-side likelihood shifts, thereby encouraging the student to learn more of the teacher's own deviation. We introduce Calibrated On-Policy Distillation (Cal-OPD), which estimates the teacher's self-deviation region through positive and negative privileged interventions and calibrates the original teacher--student discrepancy by retaining only the component that lies beyond this region. Experiments on mathematical reasoning benchmarks show that, while retaining only about 52--65\% of the original teacher--student discrepancy as the optimization signal, Cal-OPD consistently outperforms standard OPD and its variants across model scales.