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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Reinforcement Learning via Self-Distillation
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abstract
Large language models are increasingly post-trained with reinforcement learning in verifiable domains such as code and math. Yet, current methods for reinforcement learning with verifiable rewards (RLVR) learn only from a scalar outcome reward per attempt, creating a severe credit-assignment bottleneck. Many verifiable environments actually provide rich textual feedback, such as runtime errors or judge evaluations, that explain why an attempt failed. We formalize this setting as reinforcement learning with rich feedback and introduce Self-Distillation Policy Optimization (SDPO), which converts tokenized feedback into a dense learning signal without any external teacher or explicit reward model. SDPO treats the current model conditioned on feedback as a self-teacher and distills its feedback-informed next-token predictions back into the policy. In this way, SDPO leverages the model's ability to retrospectively identify its own mistakes in-context. Across scientific reasoning, tool use, and competitive programming on LiveCodeBench v6, SDPO improves sample efficiency and final accuracy over strong RLVR baselines. Notably, SDPO also outperforms baselines in standard RLVR environments that only return scalar feedback by using successful rollouts as implicit feedback for failed attempts. Finally, applying SDPO to individual questions at test time accelerates discovery on difficult binary-reward tasks, achieving the same discovery probability as best-of-k sampling or multi-turn conversations with 3x fewer attempts.
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- abstract Large language models are increasingly post-trained with reinforcement learning in verifiable domains such as code and math. Yet, current methods for reinforcement learning with verifiable rewards (RLVR) learn only from a scalar outcome reward per attempt, creating a severe credit-assignment bottleneck. Many verifiable environments actually provide rich textual feedback, such as runtime errors or judge evaluations, that explain why an attempt failed. We formalize this setting as reinforcement learning with rich feedback and introduce Self-Distillation Policy Optimization (SDPO), which converts
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2026 129representative citing papers
CL-Bench is the first expert-validated benchmark for continual learning in frontier LLMs across six real-world domains, showing limited gains and that naive in-context learning outperforms dedicated memory systems.
L-layer transformers under Log-ICoT curriculum provably learn k-parity with poly(n) samples and log k stages, matching explicit CoT efficiency without inference overhead.
Privileged-context on-policy self-distillation degrades thinking models' long-budget accuracy by suppressing forking and self-correction behaviors, while helping instruction-tuned models.
QVal is a new evaluation framework that directly measures dense supervision quality via Q-alignment to a reference policy, showing simple prompting baselines outperform 21 other methods across environments and models.
Introduces the Generalization Spectrum evaluation framework to track per-example generalization across transfer distances in competitive programming tasks.
TheoremGraph builds a unified statement-level dependency graph across informal arXiv math and formal Lean code via parsing, embeddings, and LLM validation, releasing the data and APIs for search and retrieval.
SAGE-OPD improves multi-turn OPD via turn-level selective intervention, teacher-confidence weighting, and loss normalization, reporting up to 13.3% relative gain in ALFWorld unseen success rate over standard OPD.
DRL trains a discriminator on data versus base-model samples in pretrained representation space and uses its logit as reward in KL-regularized RL, cutting guidance-free FID from 9.38 to 2.62 on SiT and similar gains on other backbones.
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.
d-OPSD reframes on-policy self-distillation for dLLMs via suffix conditioning from self-generated answers and step-level supervision, outperforming RLVR and SFT on reasoning benchmarks with ~10% of the optimization steps.
RGSD distills rubric-conditioned teacher distributions into base policies token-by-token, matching GRPO rubric satisfaction on Qwen models with one rollout and zero verifier calls.
Self-distillation from a caption-conditioned video diffusion model to an image-and-prompt-conditioned executor, enhanced by RL from VLM feedback, enables task solving in world models.
OPRD performs distillation in hidden-state space on on-policy data for deterministic gradients and better math benchmark performance, plus OPRD-Bridge for cross-architecture transfer via low-rank projectors.
DistIL applies distributional DAgger with forward cross-entropy to achieve monotonic policy improvement and better Pass@N from rich feedback in RL for reasoning tasks.
OmniOPD replaces token-level logit matching in on-policy distillation with Monte Carlo chunk-level semantic verification and a peak-entropy scheduler.
OPD+ removes the bias from stop-gradient in on-policy distillation by deriving correct gradients for f-divergences, outperforming standard KL-based methods on math reasoning and tool-use tasks.
EST-PRM stress-tests five PRM models on 4,687 reasoning chains from MATH-500, GSM8K, and PRMBench using three label-preserving transformations and reports model-specific vulnerability patterns.
DecomposeRL uses GRPO-based RL on a curated 5K-claim subset to train a decomposition policy that achieves 86.3 in-domain and 69.8 out-of-domain balanced accuracy on 11 benchmarks, supporting semi-supervised learning.
MCPO applies contrastive learning to GRPO-style RL by treating cross-domain correct rollouts as positives and incorrect ones as negatives to improve multi-domain reasoning performance in LRMs.
EDGE-OPD adds guided rollouts and evidence masking to on-policy self-distillation, enabling successful learning of target identities where standard OPSD and RLSD fail.
CEPO sharpens token credit in RLVR by requiring tokens to be favored by the correct answer and disfavored by wrong answers drawn from rejected rollouts, delivering accuracy gains on five multimodal math benchmarks.
Next-acceleration-scale autoregressive prediction in discrete latent space with on-policy privileged information distillation yields improved MRI reconstructions from sparse measurements on the fastMRI benchmark.
citing papers explorer
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Behavior Cloning is Not All You Need: The Optimality of On-Policy Distillation for Noisy Expert Feedback
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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Continual Learning Bench: Evaluating Frontier AI Systems in Real-World Stateful Environments
CL-Bench is the first expert-validated benchmark for continual learning in frontier LLMs across six real-world domains, showing limited gains and that naive in-context learning outperforms dedicated memory systems.
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Transformers Provably Learn to Internalize Chain-of-Thought
L-layer transformers under Log-ICoT curriculum provably learn k-parity with poly(n) samples and log k stages, matching explicit CoT efficiency without inference overhead.
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Rethinking On-Policy Self-Distillation for Thinking Models
Privileged-context on-policy self-distillation degrades thinking models' long-budget accuracy by suppressing forking and self-correction behaviors, while helping instruction-tuned models.
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QVal: Cheaply Evaluating Dense Supervision Signals for Long-Horizon LLM Agents
QVal is a new evaluation framework that directly measures dense supervision quality via Q-alignment to a reference policy, showing simple prompting baselines outperform 21 other methods across environments and models.
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The Generalization Spectrum: A Chromatographic Approach to Evaluating Learning Algorithms
Introduces the Generalization Spectrum evaluation framework to track per-example generalization across transfer distances in competitive programming tasks.
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TheoremGraph: Bridging Formal and Informal Mathematics
TheoremGraph builds a unified statement-level dependency graph across informal arXiv math and formal Lean code via parsing, embeddings, and LLM validation, releasing the data and APIs for search and retrieval.
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SAGE-OPD: Selective Agent-Guided Intervention for Multi-Turn On-Policy Distillation
SAGE-OPD improves multi-turn OPD via turn-level selective intervention, teacher-confidence weighting, and loss normalization, reporting up to 13.3% relative gain in ALFWorld unseen success rate over standard OPD.
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The Reward Was in Your Data All Along: Correcting Flow Matching with Discriminator-Guided RL
DRL trains a discriminator on data versus base-model samples in pretrained representation space and uses its logit as reward in KL-regularized RL, cutting guidance-free FID from 9.38 to 2.62 on SiT and similar gains on other backbones.
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Learning from Own Solutions: Self-Conditioned Credit Assignment for Reinforcement Learning with Verifiable Rewards
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.
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Zone of Proximal Policy Optimization: Teacher in Prompts, Not Gradients
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.
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Learning from the Self-future: On-policy Self-distillation for dLLMs
d-OPSD reframes on-policy self-distillation for dLLMs via suffix conditioning from self-generated answers and step-level supervision, outperforming RLVR and SFT on reasoning benchmarks with ~10% of the optimization steps.
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Rubric-Guided Self-Distillation: Post-Training Without Rubric Verifiers
RGSD distills rubric-conditioned teacher distributions into base policies token-by-token, matching GRPO rubric satisfaction on Qwen models with one rollout and zero verifier calls.
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World Model Self-Distillation: Training World Models to Solve General Tasks
Self-distillation from a caption-conditioned video diffusion model to an image-and-prompt-conditioned executor, enhanced by RL from VLM feedback, enables task solving in world models.
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OPRD: On-Policy Representation Distillation
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.
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Reinforcement Learning from Rich Feedback with Distributional DAgger
DistIL applies distributional DAgger with forward cross-entropy to achieve monotonic policy improvement and better Pass@N from rich feedback in RL for reasoning tasks.
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OmniOPD: Logit-Free On-Policy Distillation via Speculative Verification
OmniOPD replaces token-level logit matching in on-policy distillation with Monte Carlo chunk-level semantic verification and a peak-entropy scheduler.
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OPD+: Rethinking the Advantage Design for On-Policy Distillation
OPD+ removes the bias from stop-gradient in on-policy distillation by deriving correct gradients for f-divergences, outperforming standard KL-based methods on math reasoning and tool-use tasks.
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EST-PRM: Stress-Testing Process Reward Models Before They Become Load-Bearing
EST-PRM stress-tests five PRM models on 4,687 reasoning chains from MATH-500, GSM8K, and PRMBench using three label-preserving transformations and reports model-specific vulnerability patterns.
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DecomposeRL: Learning to Ask Useful, Informative, and Diverse Questions for Semi-Supervised, Traceable Claim Verification
DecomposeRL uses GRPO-based RL on a curated 5K-claim subset to train a decomposition policy that achieves 86.3 in-domain and 69.8 out-of-domain balanced accuracy on 11 benchmarks, supporting semi-supervised learning.
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Harmony in Diversity: Multi-domain Contrastive Policy Optimization for Large Reasoning Models
MCPO applies contrastive learning to GRPO-style RL by treating cross-domain correct rollouts as positives and incorrect ones as negatives to improve multi-domain reasoning performance in LRMs.
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EDGE-OPD: Internalizing Privileged Context with Evidence Guided On-Policy Distillation
EDGE-OPD adds guided rollouts and evidence masking to on-policy self-distillation, enabling successful learning of target identities where standard OPSD and RLSD fail.
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CEPO: RLVR Self-Distillation using Contrastive Evidence Policy Optimization
CEPO sharpens token credit in RLVR by requiring tokens to be favored by the correct answer and disfavored by wrong answers drawn from rejected rollouts, delivering accuracy gains on five multimodal math benchmarks.
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Next-Acceleration-Scale Prediction for Autoregressive MRI Reconstruction
Next-acceleration-scale autoregressive prediction in discrete latent space with on-policy privileged information distillation yields improved MRI reconstructions from sparse measurements on the fastMRI benchmark.
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From Plans to Pixels: Learning to Plan and Orchestrate for Open-Ended Image Editing
A planner-orchestrator system learns long-horizon image editing by maximizing outcome-based rewards from a vision-language judge and refining plans from successful trajectories.
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Learning from Language Feedback via Variational Policy Distillation
VPD frames language feedback learning as variational EM so the teacher policy refines itself via trust-region updates on outcomes while the student learns dense token distributions on its own rollouts, outperforming fixed-teacher baselines on reasoning and code tasks.
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Learning, Fast and Slow: Towards LLMs That Adapt Continually
Fast-Slow Training uses context optimization as fast weights alongside parameter updates as slow weights to achieve up to 3x better sample efficiency, higher performance, and less catastrophic forgetting than standard RL in continual LLM learning.
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Learning Agentic Policy from Action Guidance
ActGuide-RL uses human action data as plan-style guidance in mixed-policy RL to overcome exploration barriers in LLM agents, matching SFT+RL performance on search benchmarks without cold-start training.
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From Generic Correlation to Input-Specific Credit in On-Policy Self Distillation
Self-distillation token rewards measure input-response-feedback pointwise mutual information, and CREDIT extracts the input-specific component with contrastive baselines to improve LLM reasoning performance.
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Unmasking On-Policy Distillation: Where It Helps, Where It Hurts, and Why
Distillation signals align better with ideal updates on incorrect student rollouts than correct ones, with optimal teacher context depending on student capacity and task.
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Rebellious Student: Reversing Teacher Signals for Reasoning Exploration with Self-Distilled RLVR
RLRT augments GRPO by reinforcing tokens on correct student rollouts that the teacher would not have predicted, outperforming standard self-distillation and exploration baselines on Qwen3 models.
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TRACE: Distilling Where It Matters via Token-Routed Self On-Policy Alignment
TRACE improves math reasoning by distilling only on annotator-marked critical spans with forward KL on correct key spans, optional reverse KL on errors, and GRPO elsewhere, gaining 2.76 points over GRPO while preserving OOD performance.
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TAD: Temporal-Aware Trajectory Self-Distillation for Fast and Accurate Diffusion LLM
TAD improves the accuracy-parallelism trade-off in diffusion LLMs via temporal-aware self-distillation that applies hard labels to soon-to-be-decoded tokens and soft supervision to future tokens.
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KL for a KL: On-Policy Distillation with Control Variate Baseline
vOPD stabilizes on-policy distillation gradients by subtracting a closed-form per-token negative reverse KL baseline as a detached control variate, preserving unbiasedness while lowering variance and matching expensive full-vocabulary methods.
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Preference-Based Self-Distillation: Beyond KL Matching via Reward Regularization
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.
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MAD-OPD: Breaking the Ceiling in On-Policy Distillation via Multi-Agent Debate
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.
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Learn where to Click from Yourself: On-Policy Self-Distillation for GUI Grounding
GUI-SD introduces on-policy self-distillation with visually enriched privileged context and entropy-guided weighting, outperforming GRPO and naive OPSD on six GUI grounding benchmarks while improving training efficiency.
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Near-Future Policy Optimization
NPO uses a policy's own near-future checkpoint as auxiliary trajectories to maximize effective learning signal S = Q/V, improving performance from 57.88 to 63.15 on Qwen3-VL-8B-Instruct with GRPO while accelerating convergence.
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$\pi$-Play: Multi-Agent Self-Play via Privileged Self-Distillation without External Data
Self-play’s natural question-construction paths supply free privileged information that turns sparse-reward self-play into dense self-distillation, yielding stronger data-free search agents.
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Demystifying OPD: Length Inflation and Stabilization Strategies for Large Language Models
OPD for LLMs suffers length inflation and repetition collapse; StableOPD uses reference divergence and rollout mixing to prevent it and improve math reasoning performance by 7.2% on average.
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Retrieval Augmented Conversational Recommendation with Reinforcement Learning
RAR retrieves candidate items from a 300k-movie corpus then uses LLM generation with RL feedback to produce context-aware recommendations that outperform baselines on benchmarks.
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Self-Distilled RLVR
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.
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Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models
A single LLM improves its own reasoning by self-distilling from privileged verified traces as teacher to its question-only student policy, outperforming off-policy distillation and RL on math benchmarks with better token efficiency.
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DemoPSD: Disagreement-Modulated Policy Self-Distillation
Disagreement-modulated reverse-KL barycenter targets let on-policy self-distillation attenuate privileged leakage while preserving exploration, beating SDPO and GRPO on SciKnowEval and GPQA.
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When Does Continual Learning Require Learning
Different patterns of environmental change (space vs time) require different LLM update behaviors; no single family of methods—prompts, distillation, RL, or compression—handles all regimes.
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Geometric Self-Distillation for Reasoning Generalization
A geometric self-distillation objective using Hellinger loss and Fisher-Rao proximal regularization prevents predictive drift in LLM post-training, improving out-of-distribution reasoning by 5.7-8.6 points.
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Weak-to-Strong Generalization via Direct On-Policy Distillation
Transferring a weak model’s RL-induced log-ratio policy shift on a strong student’s own rollouts raises AIME accuracy more cheaply than imitating the weak teacher or running matched-step RL on the student.
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Teach-to-Reason: Competition-Guided Reasoning with a Self-Improving Teacher
T2R proposes a self-improving Teacher and competition-guided Reasoner with case-wise rewards to provide more effective supervision for CoT optimization in CXR VQA.
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ReNIO: Reweighting Negative Trajectory Importance for LLM On-Policy Distillation
ReNIO reweights negative student-generated trajectories in LLM on-policy distillation using probability ratios, reporting relative gains up to 10% on reasoning benchmarks.
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VERITAS: Verifier-Guided Proof Search for Zero-Shot Formal Theorem Proving
VERITAS improves zero-shot formal theorem proving to 40.6% on miniF2F and 7.3% on a new combinatorics benchmark by routing verifier signals into a two-phase Best-of-N then critic-guided MCTS protocol.