# Train at Moving Edge: Online-Verified Prompt Selection for Efficient RL Training of Large Reasoning Model

arXiv: https://arxiv.org/abs/2603.25184 · HTML: https://mlsanity.com/paper/2603.25184/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 29 of its 77 references that are in the map.
- First posted on arXiv 26 Mar 2026.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [PyTorch FSDP: Experiences on Scaling Fully Sharded Data Parallel](https://mlsanity.com/paper/2304.11277/) (2023)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [MM-Eureka: Exploring the Frontiers of Multimodal Reasoning with Rule-based Reinforcement Learning](https://mlsanity.com/paper/2503.07365/) (2025)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization](https://mlsanity.com/paper/2501.03262/) (2025)
- [Evaluating the Performance of Large Language Models on GAOKAO Benchmark](https://mlsanity.com/paper/2305.12474/) (2023)
- [LIMR: Less is More for RL Scaling](https://mlsanity.com/paper/2502.11886/) (2025)
- [A Comprehensive Survey in LLM(-Agent) Full Stack Safety: Data, Training and Deployment](https://mlsanity.com/paper/2504.15585/) (2025)
- [Self-Evolving Curriculum for LLM Reasoning](https://mlsanity.com/paper/2505.14970/) (2025)
- [Back to Basics: Revisiting REINFORCE Style Optimization for Learning from Human Feedback in LLMs](https://mlsanity.com/paper/2402.14740/) (2024)
- [What's Behind PPO's Collapse in Long-CoT? Value Optimization Holds the Secret](https://mlsanity.com/paper/2503.01491/) (2025)
- [Efficient Reinforcement Finetuning via Adaptive Curriculum Learning](https://mlsanity.com/paper/2504.05520/) (2025)
- [Concise Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2504.05185/) (2025)
- [SRPO: A Cross-Domain Implementation of Large-Scale Reinforcement Learning on LLM](https://mlsanity.com/paper/2504.14286/) (2025)
- [RePO: Replay-Enhanced Policy Optimization](https://mlsanity.com/paper/2506.09340/) (2025)
- [RLEP: Reinforcement Learning with Experience Replay for LLM Reasoning](https://mlsanity.com/paper/2507.07451/) (2025)
- [Beyond Correctness: Harmonizing Process and Outcome Rewards through RL Training](https://mlsanity.com/paper/2509.03403/) (2025)
- [MAPO: Mixed Advantage Policy Optimization](https://mlsanity.com/paper/2509.18849/) (2025)
- [LSPO: Length-aware Dynamic Sampling for Policy Optimization in LLM Reasoning](https://mlsanity.com/paper/2510.01459/) (2025)
- [No More Stale Feedback: Co-Evolving Critics for Open-World Agent Learning](https://mlsanity.com/paper/2601.06794/) (2026)
- [Learning Dynamics in RL Post-Training for Language Models](https://mlsanity.com/paper/2601.04670/) (2026)

## Built on by (most cited first, 10 of 10)

- [Policy and World Modeling Co-Training for Language Agents](https://mlsanity.com/paper/2606.02388/) (2026)
- [AHD Agent: Agentic Reinforcement Learning for Automatic Heuristic Design](https://mlsanity.com/paper/2605.08756/) (2026)
- [GD2PO: Mitigating Multi-Reward Conflicts via Group-Dynamic reward-Decoupled Policy Optimization](https://mlsanity.com/paper/2606.16771/) (2026)
- [Beyond Solvability: Task Learnability as a Static Prior for LLM RL Post-Training](https://mlsanity.com/paper/2608.09217/) (2026)
- [Cooperative Coevolution for Resource-Constrained Agentic LLM Post-Training](https://mlsanity.com/paper/2608.02391/) (2026)
- [Act More, Decide Less: Skill-Guided Adaptive Action Chunking for Long-Horizon LLM Agents](https://mlsanity.com/paper/2609.02042/) (2026)
- [Gradient Extrapolation-Based Policy Optimization](https://mlsanity.com/paper/2605.06755/) (2026)
- [AdaKP: Online Adaptive Knowledge-Point Selection for Reasoning-Oriented Reinforcement Learning](https://mlsanity.com/paper/2607.24833/) (2026)
- [Rollout Efficiency in Reinforcement Learning for Reasoning Large Language Models: A Taxonomy and Future Directions](https://mlsanity.com/paper/2609.25463/) (2026)
- [Selecting Diverse SFT Traces Improves Post-RL Generalization](https://mlsanity.com/paper/2609.33780/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) has become essential for post-training large language models (LLMs) in reasoning tasks. While scaling rollouts can stabilize training and enhance performance, the computational overhead is a critical issue. In algorithms like GRPO, multiple rollouts per prompt incur prohibitive costs, as a large portion of prompts provide negligible gradients and are thus of low utility. To address this problem, we investigate how to select high-utility prompts before the rollout phase. Our experimental analysis reveals that sample utility is non-uniform and evolving: the strongest learning signals concentrate at the ``learning edge", the intersection of intermediate difficulty and high uncertainty, which shifts as training proceeds. Motivated by this, we propose HIVE (History-Informed and online-VErified prompt selection), a dual-stage framework for data-efficient RL. HIVE utilizes historical reward trajectories for coarse selection and employs prompt entropy as a real-time proxy to prune instances with stale utility. By evaluating HIVE across multiple math reasoning benchmarks and models, we show that HIVE yields significant rollout efficiency without compromising performance.