---
title: "Reinforcement Learning for Reasoning in Small LLMs: What"
description: "The study offers an affordable, reproducible path to better reasoning in compact models, with open… 45 references, cited by 37 papers here."
authors: ["Quy-Anh Dang", "Chris Ngo"]
year: 2025
venue: "arXiv:2503.16219"
source: "https://arxiv.org/abs/2503.16219"
doi: "10.48550/arxiv.2503.16219"
arxiv: "2503.16219"
licence: "CC BY 4.0 (arXiv)"
licence_url: "http://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/dang-2025-reinforcement-learning-reasoning-small-llms/"
---
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# Reinforcement Learning for Reasoning in Small LLMs: What Works and What Doesn't

**Authors:** Quy-Anh Dang and Chris Ngo · **Year:** 2025 · **Venue:** arXiv:2503.16219 · **Licence:** [CC BY 4.0 (arXiv)](http://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2503.16219) · [PDF](https://arxiv.org/pdf/2503.16219) · [DOI 10.48550/arxiv.2503.16219](https://doi.org/10.48550/arxiv.2503.16219) · [arXiv 2503.16219](https://arxiv.org/abs/2503.16219) · [OpenAlex](https://openalex.org/W4415288811)

**Citations:** 0 citations (OpenAlex, 2026-10-14) · [37](https://md.research.elamur.ai/free/en/papers/dang-2025-reinforcement-learning-reasoning-small-llms/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
The paper tests whether reinforcement learning can substantially improve mathematical reasoning in a small language model on a tight compute budget. The authors train DeepSeek-R1-Distill-Qwen-1.5B directly with GRPO, skipping supervised fine-tuning, on four NVIDIA A40 GPUs for no more than 24 hours. Training data come from two existing collections, s1 and DeepScaleR, filtered down to non-trivial math problems. Rewards are entirely rule-based: answer correctness, a length-sensitive cosine variant, and a check for thinking tags. Across three experiments, the selected checkpoints (released as Open-RS1, Open-RS2 and Open-RS3) improve quickly within 50–100 steps. AMC23 accuracy rises from 63% to 80%, and AIME24 reaches 46.7%, which beats o1-preview. A full run costs about $42, compared with thousands of dollars for similar 1.5B and 7B baselines. Longer training, however, causes instability, runs into completion-length limits and produces mixed-language output. The study offers an affordable, reproducible path to better reasoning in compact models, with open code and data.

## Key points
- **Data:** filtering yields open-s1 (18,615 examples) and open-deepscaler (21,044), totalling 39,659 math questions. Only about 7,000 samples, with 6 outputs each, are actually used in training.
- **Method:** GRPO, which needs no critic model, combined with accuracy, cosine-length and format rewards. A system-prompt instruction to answer in English stands in for a costly language reward.
- **Scores (zero-shot pass@1):**
  - Average scores are 53.0% (Open-RS1), 55.7% (Open-RS2) and 56.3% (Open-RS3), versus 57.0% for DeepScaleR-1.5B-Preview.
  - Open-RS3 reaches 46.7% on AIME24, ahead of o1-preview (44.6%).
- **Cost:** about $42 on 4× A40 for 24h. Reported baselines cost $3629 (DeepScaleR-1.5B-Preview), $2268 (Still-3-1.5B-Preview) and $1633 (Qwen2.5-7B-SimpleRL).
- **Limitations and release:** gains fade with prolonged training, Minerva scores trail 7B models, and multilingual drift persists. Code and datasets are available at github.com/knoveleng/open-rs.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

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## Cite

Cite as: Quy-Anh Dang and Chris Ngo. 2025. Reinforcement Learning for Reasoning in Small LLMs: What Works and What Doesn't. arXiv:2503.16219.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{dang2025reinforcement,
  title = {{Reinforcement Learning for Reasoning in Small LLMs: What Works and What Doesn't}},
  author = {Quy-Anh Dang and Chris Ngo},
  year = {2025},
  doi = {10.48550/arxiv.2503.16219},
  eprint = {2503.16219},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2503.16219}
}
```

- [← previous RedStar: Does Scaling Long-CoT Data Unlock Better Slow-Reasoning Systems?](https://md.research.elamur.ai/free/en/papers/xu-2025-redstar-scaling-long-cot-data/)
- [next → SFT or RL? An Early Investigation into Training R1-Like Reasoning Large Vision-Language Models](https://md.research.elamur.ai/free/en/papers/chen-2025-sft-rl-early-investigation-training/)
- [↑ back to papers of 2025](https://md.research.elamur.ai/free/en/papers/2025/page/4/)

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45. Contents \#\# Introduction Methodology High-Quality Dataset Curation . . . . . . . . . . Reinforcement Learning Algorithm . . . . . . . . 2 2 3 [find](https://scholar.google.com/scholar?q=Contents+%5C%23%5C%23+Introduction+Methodology+High%2DQuality+Dataset+Curation+%2E+%2E+%2E+%2E+%2E+%2E+%2E+%2E+%2E+%2E+Reinforcement+Learning+Algorithm+%2E+%2E+%2E+%2E+%2E+%2E+%2E+%2E+2+2+3)

*Updated 3 November 2026*