# Off-Context GRPO: Learning to Reason on Hard Problems using Privileged Information

arXiv: https://arxiv.org/abs/2607.19313 · HTML: https://mlsanity.com/paper/2607.19313/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 38 of its 46 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 38)

- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [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)
- [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)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [Trial and Error: Exploration-Based Trajectory Optimization for LLM Agents](https://mlsanity.com/paper/2403.02502/) (2024)
- [Evaluating the Performance of Large Language Models on GAOKAO Benchmark](https://mlsanity.com/paper/2305.12474/) (2023)
- [Self-Evolving Curriculum for LLM Reasoning](https://mlsanity.com/paper/2505.14970/) (2025)
- [On-Policy RL Meets Off-Policy Experts: Harmonizing Supervised Fine-Tuning and Reinforcement Learning via Dynamic Weighting](https://mlsanity.com/paper/2508.11408/) (2025)
- [BREAD: Branched Rollouts from Expert Anchors Bridge SFT & RL for Reasoning](https://mlsanity.com/paper/2506.17211/) (2025)
- [Blending Supervised and Reinforcement Fine-Tuning with Prefix Sampling](https://mlsanity.com/paper/2507.01679/) (2025)
- [ExGRPO: Learning to Reason from Experience](https://mlsanity.com/paper/2510.02245/) (2025)
- [Scaf-GRPO: Scaffolded Group Relative Policy Optimization for Enhancing LLM Reasoning](https://mlsanity.com/paper/2510.19807/) (2025)
- [DUMP: Automated Distribution-Level Curriculum Learning for RL-based LLM Post-training](https://mlsanity.com/paper/2504.09710/) (2025)
- [Depth-Breadth Synergy in RLVR: Unlocking LLM Reasoning Gains with Adaptive Exploration](https://mlsanity.com/paper/2508.13755/) (2025)
- [POPE: Learning to Reason on Hard Problems via Privileged On-Policy Exploration](https://mlsanity.com/paper/2601.18779/) (2026)
- [StepHint: Multi-level Stepwise Hints Enhance Reinforcement Learning to Reason](https://mlsanity.com/paper/2507.02841/) (2025)
- [VCRL: Variance-based Curriculum Reinforcement Learning for Large Language Models](https://mlsanity.com/paper/2509.19803/) (2025)
- [GATES: Self-Distillation under Privileged Context with Consensus Gating](https://mlsanity.com/paper/2602.20574/) (2026)

## Built on by (most cited first, 7 of 7)

- [The Model Knows Another Way: Strategy Switching for Effective RLVR Exploration](https://mlsanity.com/paper/2609.33085/) (2026)
- [RLTL;DR: Self-improvement by Internalizing Self-generated Feedback](https://mlsanity.com/paper/2609.37633/) (2026)
- [Unlearnable, or Unmeasured? On the Reliability of Difficulty Labels in RLVR](https://mlsanity.com/paper/2609.40115/) (2026)
- [Hints, Critics, and Teachers: Prior Injection for Sparse-Reward RL in Vision-Language Math Reasoning](https://mlsanity.com/paper/2608.21811/) (2026)
- [Save Your Saturated Data: Learning Beyond Reward Saturation in Group-Based RL](https://mlsanity.com/paper/2609.33126/) (2026)
- [RAISE: Reinforcing Access Control Policy Synthesis in LLMs via Symbolic Evaluation](https://mlsanity.com/paper/2609.33796/) (2026)
- [Understanding Enrichment in Reinforcement Learning](https://mlsanity.com/paper/2610.02846/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) improves reasoning in large language models. Yet, typical RLVR approaches fail on difficult problems: when a model cannot generate any correct solutions, it receives textitzero learning signal. Providing privileged guidance during training, such as solution prefixes, can help overcome this learning cliff by steering the model towards correct solutions with non-zero reward. We call these rollouts textitoff-context: they are generated from a training prompt that contains privileged guidance, while the target objective is defined by the original prompt without that guidance. We introduce Off-Context GRPO (OC-GRPO), a minimally modified variant of GRPO that uses guided rollouts but applies an importance-corrected objective to steer the update back toward the original unguided objective, avoiding the mismatch that destabilizes uncorrected guided training. Empirically, our algorithm achieves a 3.8% absolute improvement (13.7% relative gain) over vanilla GRPO on average across standard mathematical reasoning benchmarks with negligible additional cost.