# Self-Hinting Language Models Enhance Reinforcement Learning

arXiv: https://arxiv.org/abs/2602.03143 · HTML: https://mlsanity.com/paper/2602.03143/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 28 of its 37 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 28 of 28)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [RLHF Workflow: From Reward Modeling to Online RLHF](https://mlsanity.com/paper/2405.07863/) (2024)
- [A Minimalist Approach to LLM Reasoning: from Rejection Sampling to Reinforce](https://mlsanity.com/paper/2504.11343/) (2025)
- [Reward-Guided Speculative Decoding for Efficient LLM Reasoning](https://mlsanity.com/paper/2501.19324/) (2025)
- [Scaf-GRPO: Scaffolded Group Relative Policy Optimization for Enhancing LLM Reasoning](https://mlsanity.com/paper/2510.19807/) (2025)
- [StepHint: Multi-level Stepwise Hints Enhance Reinforcement Learning to Reason](https://mlsanity.com/paper/2507.02841/) (2025)
- [Improving Sampling Efficiency in RLVR through Adaptive Rollout and Response Reuse](https://mlsanity.com/paper/2509.25808/) (2025)
- [The Crucial Role of Samplers in Online Direct Preference Optimization](https://mlsanity.com/paper/2409.19605/) (2024)
- [Reinforce-Ada: An Adaptive Sampling Framework under Non-linear RL Objectives](https://mlsanity.com/paper/2510.04996/) (2025)
- [Optimizing Chain-of-Thought Reasoners via Gradient Variance Minimization in Rejection Sampling and RL](https://mlsanity.com/paper/2505.02391/) (2025)
- [Knapsack RL: Unlocking Exploration of LLMs via Optimizing Budget Allocation](https://mlsanity.com/paper/2509.25849/) (2025)
- [PILAF: Optimal Human Preference Sampling for Reward Modeling](https://mlsanity.com/paper/2502.04270/) (2025)

## Built on by (most cited first, 20 of 20)

- [Multi-Turn On-Policy Distillation with Prefix Replay](https://mlsanity.com/paper/2607.04763/) (2026)
- [Learning to Hint for Reinforcement Learning](https://mlsanity.com/paper/2604.00698/) (2026)
- [VISD: Enhancing Video Reasoning via Structured Self-Distillation](https://mlsanity.com/paper/2605.06094/) (2026)
- [KnowRL: Boosting LLM Reasoning via Reinforcement Learning with Minimal-Sufficient Knowledge Guidance](https://mlsanity.com/paper/2604.12627/) (2026)
- [Large Language Model Post-Training: A Unified View of Off-Policy and On-Policy Learning](https://mlsanity.com/paper/2604.07941/) (2026)
- [Nudging Beyond the Comfort Zone: Efficient Strategy-Guided Exploration for RLVR](https://mlsanity.com/paper/2605.15726/) (2026)
- [Agent Explorative Policy Optimization for Multimodal Agentic Reasoning](https://mlsanity.com/paper/2605.28774/) (2026)
- [Maximizing Rollout Informativeness under a Fixed Budget: A Submodular View of Tree Search for Tool-Use Agentic Reinforcement Learning](https://mlsanity.com/paper/2605.05262/) (2026)
- [Instruction-Conditioned Exploration for Reinforcement Learning with Self-Distillation to an Unconditioned Policy](https://mlsanity.com/paper/2608.02087/) (2026)
- [Negative Self-Distillation: Learning to Reason by Avoiding Flaws](https://mlsanity.com/paper/2609.11699/) (2026)
- [Rollout Pass-Rate Control: Steering Binary-Reward RL Toward Its Most Informative Regime](https://mlsanity.com/paper/2605.05112/) (2026)
- [Seirenes: Adversarial Self-Play with Evolving Distractions for LLM Reasoning](https://mlsanity.com/paper/2605.11636/) (2026)
- [Intrinsic Selection and Particle Resampling for Inference-Time Scaling Beyond Domain Verifiability](https://mlsanity.com/paper/2606.08850/) (2026)
- [SCOPE-RL: Optimizing Reasoning Paths Before and After Success](https://mlsanity.com/paper/2607.11506/) (2026)
- [TD-Grokking: Learning from Zero-Reward Problems by Training-Time Decomposition](https://mlsanity.com/paper/2606.09883/) (2026)
- [LoRA Scaffolded Policy Optimization (LSPO): A Sampling-Time Low-Rank Scaffold for Recovering Reinforcement-Learning Gradient on Zero-Reward Cliff Prompts](https://mlsanity.com/paper/2607.27787/) (2026)
- [ARC: Fair Relative Advantage Comparison in Open-Ended Real-World Interaction](https://mlsanity.com/paper/2608.13622/) (2026)
- [Teach to Learn: Hint Annealing for Self-improving LLM Reasoning](https://mlsanity.com/paper/2609.34975/) (2026)
- [Balancing Reference Guidance and Free Generation in Trajectory Rollouts for Reasoning RL](https://mlsanity.com/paper/2610.11128/) (2026)
- [Variance-Optimal State Resampling for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2610.15888/) (2026)

## Abstract (arXiv)

Group Relative Policy Optimization (GRPO) has recently emerged as a practical recipe for aligning large language models with verifiable objectives. However, under sparse terminal rewards, GRPO often stalls because rollouts within a group frequently receive identical rewards, causing relative advantages to collapse and updates to vanish. We propose self-hint aligned GRPO with privileged supervision (SAGE), an on-policy reinforcement learning framework that injects privileged hints during training to reshape the rollout distribution under the same terminal verifier reward. For each prompt x, the model samples a compact hint h (e.g., a plan or decomposition) and then generates a solution τ conditioned on (x,h). Crucially, the task reward R(x,τ) is unchanged; hints only increase within-group outcome diversity under finite sampling, preventing GRPO advantages from collapsing under sparse rewards. At test time, we set h=varnothing and deploy the no-hint policy without any privileged information. Moreover, sampling diverse self-hints serves as an adaptive curriculum that tracks the learner's bottlenecks more effectively than fixed hints from an initial policy or a stronger external model. Experiments over 6 benchmarks with 3 LLMs show that SAGE consistently outperforms GRPO, on average +2.0 on Llama-3.2-3B-Instruct, +1.2 on Qwen2.5-7B-Instruct and +1.3 on Qwen3-4B-Instruct. The code is available at https://github.com/BaohaoLiao/SAGE.