MOPD improves on-policy distillation for LLMs by using peer successes for positive patterns and failures for negative examples to create more informative teacher signals.
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Learning to Reason under Off-Policy Guidance
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abstract
Recent advances in large reasoning models (LRMs) demonstrate that sophisticated behaviors such as multi-step reasoning and self-reflection can emerge via reinforcement learning with verifiable rewards~(\textit{RLVR}). However, existing \textit{RLVR} approaches are inherently ``on-policy'', limiting learning to a model's own outputs and failing to acquire reasoning abilities beyond its initial capabilities. To address this issue, we introduce \textbf{LUFFY} (\textbf{L}earning to reason \textbf{U}nder o\textbf{FF}-polic\textbf{Y} guidance), a framework that augments \textit{RLVR} with off-policy reasoning traces. LUFFY dynamically balances imitation and exploration by combining off-policy demonstrations with on-policy rollouts during training. Specifically, LUFFY combines the Mixed-Policy GRPO framework, which has a theoretically guaranteed convergence rate, alongside policy shaping via regularized importance sampling to avoid superficial and rigid imitation during mixed-policy training. Compared with previous RLVR methods, LUFFY achieves an over \textbf{+6.4} average gain across six math benchmarks and an advantage of over \textbf{+6.2} points in out-of-distribution tasks. Most significantly, we show that LUFFY successfully trains weak models in scenarios where on-policy RLVR completely fails. These results provide compelling evidence that LUFFY transcends the fundamental limitations of on-policy RLVR and demonstrates the great potential of utilizing off-policy guidance in RLVR.
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representative citing papers
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.
The cumulative token IS ratio gives unbiased prefix correction and lower variance than full-sequence ratios for token-level gradients in LLM policy optimization, enabling CTPO to outperform GRPO and GSPO baselines on mathematical reasoning tasks.
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.
NExt accelerates RLVR training for LLMs by nonlinearly extrapolating low-rank parameter trajectories extracted from LoRA runs.
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.
GPS trains a small model on optimization history to predict prompt difficulty and select intermediate-difficulty diverse batches, yielding better training efficiency, final performance, and test-time allocation than baselines on reasoning benchmarks.
Prefix-RFT blends SFT and RFT via prefix sampling from demonstrations to outperform standalone SFT, RFT, and mixed-policy baselines on math reasoning problems.
DelTA estimates token coefficients to amplify discriminative directions in token-gradient vectors, reweighting the RLVR surrogate to produce more contrastive side-wise centroids and yielding 3.26 and 2.62 point gains on math benchmarks for 8B and 14B Qwen3 models.
DMPO approximates forward KL minimization in on-policy RL by aligning the policy to a group-level reward-proportional target distribution, yielding 9-12% relative gains over GRPO on NP-Bench and smaller gains on math reasoning.
HASP upgrades textual skills into executable Program Functions that intervene in LLM agent loops at inference, post-training, or self-evolution, delivering 25% gains over ReAct and 30.4% over Search-R1 on reasoning benchmarks.
VSPO samples rollouts at varying steering intensities to improve behavioral control in LLMs while preserving task accuracy.
STRIDE co-trains generator and verifier on outcome rewards alone to deliver learnable stepwise language feedback that redirects LLM reasoning trajectories and outperforms scalar-reward baselines.
TGPO improves on-policy LLM distillation by using teacher predictions conditioned on student rollouts to supply informative guidance when the two distributions diverge.
Seirênes trains LLMs via adversarial self-play to generate and overcome evolving distractions, producing gains of 7-10 points on math reasoning benchmarks and exposing blind spots in larger models.
Span-level Wasserstein distances between hidden-state distributions of correct and incorrect rollouts provide a self-supervised signal to reweight advantages in GRPO, improving fine-grained credit assignment on math and code tasks.
SPS interleaves RL and IRL to counteract probability squeezing in LLM reasoning trajectories, improving Pass@k on five benchmarks while identifying an empirical upper bound on multi-sample performance.
PreRL applies reward-driven updates to P(y) in pre-train space, uses Negative Sample Reinforcement to prune bad reasoning paths and boost reflection, and combines with standard RL in Dual Space RL to outperform baselines on reasoning tasks.
Lightning OPD is an offline on-policy distillation method that matches standard OPD performance at 4x efficiency by enforcing teacher consistency between SFT and distillation phases.
TensorHub uses Reference-Oriented Storage to enable scalable weight transfer in LLM RL training by referencing replicated GPU weights, achieving up to 19x reduction in cross-datacenter stall time.
Online Label Refinement lets LLMs learn robust reasoning from noisy supervision by correcting labels when majority answers show rising rollout success and stable history, delivering 3-4% gains on math and reasoning benchmarks even at high noise levels.
HAPO adds a hindsight-anchored SSI operator with Thompson gating to GRPO-style RLVR, achieving asymptotic consistency that recovers unbiased on-policy gradients as the policy improves.
ECHO jointly optimizes policy and critic via co-evolution, cascaded rollouts, and saturation-aware shaping to deliver non-stale feedback and higher success in open-world LLM agent RL.
SPHINX generates synthetic visual puzzles for benchmarking LVLMs, where GPT-5 scores 51.1% and RLVR training improves both in-domain and external visual reasoning performance.
citing papers explorer
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Multi-Rollout On-Policy Distillation via Peer Successes and Failures
MOPD improves on-policy distillation for LLMs by using peer successes for positive patterns and failures for negative examples to create more informative teacher signals.
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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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Rethinking Importance Sampling in LLM Policy Optimization: A Cumulative Token Perspective
The cumulative token IS ratio gives unbiased prefix correction and lower variance than full-sequence ratios for token-level gradients in LLM policy optimization, enabling CTPO to outperform GRPO and GSPO baselines on mathematical reasoning tasks.
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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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Low-rank Optimization Trajectories Modeling for LLM RLVR Acceleration
NExt accelerates RLVR training for LLMs by nonlinearly extrapolating low-rank parameter trajectories extracted from LoRA runs.
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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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Small Generalizable Prompt Predictive Models Can Steer Efficient RL Post-Training of Large Reasoning Models
GPS trains a small model on optimization history to predict prompt difficulty and select intermediate-difficulty diverse batches, yielding better training efficiency, final performance, and test-time allocation than baselines on reasoning benchmarks.
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Blending Supervised and Reinforcement Fine-Tuning with Prefix Sampling
Prefix-RFT blends SFT and RFT via prefix sampling from demonstrations to outperform standalone SFT, RFT, and mixed-policy baselines on math reasoning problems.
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DelTA: Discriminative Token Credit Assignment for Reinforcement Learning from Verifiable Rewards
DelTA estimates token coefficients to amplify discriminative directions in token-gradient vectors, reweighting the RLVR surrogate to produce more contrastive side-wise centroids and yielding 3.26 and 2.62 point gains on math benchmarks for 8B and 14B Qwen3 models.
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Beyond Mode Collapse: Distribution Matching for Diverse Reasoning
DMPO approximates forward KL minimization in on-policy RL by aligning the policy to a group-level reward-proportional target distribution, yielding 9-12% relative gains over GRPO on NP-Bench and smaller gains on math reasoning.
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Harnessing LLM Agents with Skill Programs
HASP upgrades textual skills into executable Program Functions that intervene in LLM agent loops at inference, post-training, or self-evolution, delivering 25% gains over ReAct and 30.4% over Search-R1 on reasoning benchmarks.
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VSPO: Vector-Steered Policy Optimization for Behavioral Control
VSPO samples rollouts at varying steering intensities to improve behavioral control in LLMs while preserving task accuracy.
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STRIDE: Learnable Stepwise Language Feedback for LLM Reasoning
STRIDE co-trains generator and verifier on outcome rewards alone to deliver learnable stepwise language feedback that redirects LLM reasoning trajectories and outperforms scalar-reward baselines.
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Teacher-Guided Policy Optimization for LLM Distillation
TGPO improves on-policy LLM distillation by using teacher predictions conditioned on student rollouts to supply informative guidance when the two distributions diverge.
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Seir\^enes: Adversarial Self-Play with Evolving Distractions for LLM Reasoning
Seirênes trains LLMs via adversarial self-play to generate and overcome evolving distractions, producing gains of 7-10 points on math reasoning benchmarks and exposing blind spots in larger models.
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Hidden States Know Where Reasoning Diverges: Credit Assignment via Span-Level Wasserstein Distance
Span-level Wasserstein distances between hidden-state distributions of correct and incorrect rollouts provide a self-supervised signal to reweight advantages in GRPO, improving fine-grained credit assignment on math and code tasks.
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SPS: Steering Probability Squeezing for Better Exploration in Reinforcement Learning for Large Language Models
SPS interleaves RL and IRL to counteract probability squeezing in LLM reasoning trajectories, improving Pass@k on five benchmarks while identifying an empirical upper bound on multi-sample performance.
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From $P(y|x)$ to $P(y)$: Investigating Reinforcement Learning in Pre-train Space
PreRL applies reward-driven updates to P(y) in pre-train space, uses Negative Sample Reinforcement to prune bad reasoning paths and boost reflection, and combines with standard RL in Dual Space RL to outperform baselines on reasoning tasks.
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Lightning OPD: Efficient Post-Training for Large Reasoning Models with Offline On-Policy Distillation
Lightning OPD is an offline on-policy distillation method that matches standard OPD performance at 4x efficiency by enforcing teacher consistency between SFT and distillation phases.
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TensorHub: Scalable and Elastic Weight Transfer for LLM RL Training
TensorHub uses Reference-Oriented Storage to enable scalable weight transfer in LLM RL training by referencing replicated GPU weights, achieving up to 19x reduction in cross-datacenter stall time.
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Can LLMs Learn to Reason Robustly under Noisy Supervision?
Online Label Refinement lets LLMs learn robust reasoning from noisy supervision by correcting labels when majority answers show rising rollout success and stable history, delivering 3-4% gains on math and reasoning benchmarks even at high noise levels.
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Hindsight-Anchored Policy Optimization: Turning Failure into Feedback in Sparse Reward Settings
HAPO adds a hindsight-anchored SSI operator with Thompson gating to GRPO-style RLVR, achieving asymptotic consistency that recovers unbiased on-policy gradients as the policy improves.
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No More Stale Feedback: Co-Evolving Critics for Open-World Agent Learning
ECHO jointly optimizes policy and critic via co-evolution, cascaded rollouts, and saturation-aware shaping to deliver non-stale feedback and higher success in open-world LLM agent RL.
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SPHINX: A Synthetic Environment for Visual Perception and Reasoning
SPHINX generates synthetic visual puzzles for benchmarking LVLMs, where GPT-5 scores 51.1% and RLVR training improves both in-domain and external visual reasoning performance.
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InternBootcamp Technical Report: Boosting LLM Reasoning with Verifiable Task Scaling
InternBootcamp supplies 1000+ verifiable, auto-generated task environments across domains that enable task scaling to improve LLM reasoning, producing a 32B model with state-of-the-art results on the new Bootcamp-EVAL benchmark.
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EvoCoT: Overcoming the Exploration Bottleneck in Reinforcement Learning
EvoCoT uses self-generated and verified CoT trajectories in a two-stage curriculum to let LLMs learn from initially unsolved hard problems in RLVR settings.
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RL-PLUS: Countering Capability Boundary Collapse of LLMs in Reinforcement Learning with Hybrid-policy Optimization
RL-PLUS is a hybrid RL approach for LLMs that combines internal exploitation with external data via importance sampling and exploration advantages to prevent capability boundary collapse and achieve gains on math and OOD reasoning benchmarks.
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FBOS-RL: Feedback-Driven Bi-Objective Synergistic Reinforcement Learning
FBOS-RL is a feedback-driven bi-objective RL framework that combines Feedback-Guided Exploration Enhancement with Exploitation-oriented Policy Alignment and Exploration-oriented Capability Cultivation to raise training speed and final performance over GRPO under fixed rollout budgets.
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OGER: A Robust Offline-Guided Exploration Reward for Hybrid Reinforcement Learning
OGER adds an auxiliary exploration reward built from offline trajectories and model entropy to hybrid RL training, yielding gains on math reasoning benchmarks and out-of-domain generalization.
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Rethinking Expert Trajectory Utilization in LLM Post-training for Mathematical Reasoning
Sequential SFT followed by RL, guided by the Plasticity-Ceiling Framework, achieves higher performance ceilings in LLM mathematical reasoning than synchronized methods by optimizing data scale and transition timing.
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Depth-Breadth Synergy in RLVR: Unlocking LLM Reasoning Gains with Adaptive Exploration
DARS adaptively increases rollouts on hard problems in RLVR to improve Pass@K, and when paired with batch scaling for breadth, achieves gains in both Pass@K and Pass@1 by treating depth and breadth as complementary exploration dimensions.
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Sample-efficient LLM Optimization with Reset Replay
LoRR augments preference optimization methods like DPO with high-replay training, periodic resets to initial data/policy, and a hybrid objective to improve sample efficiency and reduce primacy bias on math and reasoning tasks.
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EasyVideoR1: Easier RL for Video Understanding
EasyVideoR1 delivers an optimized RL pipeline for video understanding in large vision-language models, achieving 1.47x throughput gains and aligned results on 22 benchmarks.
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A Survey of On-Policy Distillation for Large Language Models
A survey that formalizes on-policy distillation as f-divergence minimization over student-sampled trajectories and organizes the literature along three design axes while linking it to KL-constrained RL.