# Cool the Sampler, Not the Learner: Sampling Temperature Moves the Staleness Cliff of Importance-Corrected GRPO

arXiv: https://arxiv.org/abs/2609.36953 · HTML: https://mlsanity.com/paper/2609.36953/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 22 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 19 of 19)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoning](https://mlsanity.com/paper/2505.24298/) (2025)
- [Prosperity before Collapse: How Far Can Off-Policy RL Reach with Stale Data on LLMs?](https://mlsanity.com/paper/2510.01161/) (2025)
- [Look Inward to Explore Outward: Learning Temperature Policy from LLM Internal States via Hierarchical RL](https://mlsanity.com/paper/2602.13035/) (2026)
- [Part II: ROLL Flash -- Accelerating RLVR and Agentic Training with Asynchrony](https://mlsanity.com/paper/2510.11345/) (2025)
- [A-3PO: Accelerating Asynchronous LLM Training with Staleness-aware Proximal Policy Approximation](https://mlsanity.com/paper/2512.06547/) (2025)
- [StaleFlow: Staleness-Aware Data Management for Mitigating Data Skewness in Fully Disaggregated RL Post-Training](https://mlsanity.com/paper/2601.12784/) (2026)
- [Stable Asynchrony: Variance-Controlled Off-Policy RL for LLMs](https://mlsanity.com/paper/2602.17616/) (2026)
- [Exploring Multi-Temperature Strategies for Token- and Rollout-Level Control in RLVR](https://mlsanity.com/paper/2510.08892/) (2025)
- [Temperature as a Meta-Policy: Adaptive Temperature in LLM Reinforcement Learning](https://mlsanity.com/paper/2602.11779/) (2026)
- [How Off-Policy Can GRPO Be? Mu-GRPO for Efficient LLM Reinforcement Learning](https://mlsanity.com/paper/2605.17570/) (2026)
- [GAC: Stabilizing Asynchronous RL Training for LLMs via Gradient Alignment Control](https://mlsanity.com/paper/2603.01501/) (2026)
- [Internalize the Temperature: On-Policy Self-Distillation as Policy Reheater for Reinforcement Learning](https://mlsanity.com/paper/2606.00755/) (2026)

## Abstract (arXiv)

Production RL for language models lets the sampler fall behind the learner and repairs the resulting mismatch with a truncated importance weight. We ask how long the sampler can go without a refresh under that correction, and find a cliff: on Qwen2.5-Math-1.5B and GSM8K, importance-corrected GRPO refreshed every 192 updates learns well for 180 steps and then degrades severely in all three data seeds before the refresh arrives. Published remedies for staleness act on the update; we act on the sampler instead. Decoupled cooling draws samples at temperature 0.8 while the learner, the reference model and the importance weights stay at temperature 1, with the behaviour probability recorded from the tempered distribution, so the learner's objective is unchanged. All corresponding cooled runs are stable, and the longer interval keeps what the short one delivered: at the same update budget, a cooled sampler refreshed every 192 steps matches an uncooled sampler refreshed every 96 at the end of training (0.857 for both) and averaged over it (0.79), whereas lowering the learning rate to a safe value ends 3-7 points lower. On Qwen2.5-Math-7B the degradation points at interval 192 predict that an interval of 144 is fatal without cooling and survivable with it; on two data seeds the uncooled runs degrade before their first refresh and the cooled runs pass it and end at 92-93% against 68-81%, with one cooled run degrading transiently late in the second cycle. The benefit has a window: at three times the safe interval and in a high-mismatch MATH setting cooling delays degradation without preventing it, stronger cooling is not better, and cooling without the correction collapses. Sampling temperature is a control on staleness tolerance, and temperature and refresh interval should be chosen together.