---
title: "Teaching Large Language Models to Reason with Reinforcement"
description: "This study asks whether reinforcement learning techniques, popularised by RLHF, can strengthen the… 77 references, cited by 58 papers here."
authors: ["Alex Havrilla", "Yuqing Du", "Sharath Chandra Raparthy", "Christoforos Nalmpantis", "Jane Dwivedi-Yu", "Maksym Zhuravinskyi", "Eric Hambro", "Sainbayar Sukhbaatar", "Roberta Raileanu"]
year: 2024
venue: "arXiv:2403.04642"
source: "https://arxiv.org/abs/2403.04642"
doi: "10.48550/arxiv.2403.04642"
arxiv: "2403.04642"
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/havrilla-2024-teaching-large-language-models-reason/"
---
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# Teaching Large Language Models to Reason with Reinforcement Learning

**Authors:** [Alex Havrilla](https://md.research.elamur.ai/free/en/authors/alex-havrilla/), Yuqing Du, [Sharath Chandra Raparthy](https://md.research.elamur.ai/free/en/authors/sharath-chandra-raparthy/), [Christoforos Nalmpantis](https://md.research.elamur.ai/free/en/authors/christoforos-nalmpantis/), [Jane Dwivedi-Yu](https://md.research.elamur.ai/free/en/authors/jane-dwivedi-yu/), [Maksym Zhuravinskyi](https://md.research.elamur.ai/free/en/authors/maksym-zhuravinskyi/), [Eric Hambro](https://md.research.elamur.ai/free/en/authors/eric-hambro/), [Sainbayar Sukhbaatar](https://md.research.elamur.ai/free/en/authors/sainbayar-sukhbaatar/) and [Roberta Raileanu](https://md.research.elamur.ai/free/en/authors/roberta-raileanu/) · **Year:** 2024 · **Venue:** arXiv:2403.04642 · **Licence:** [CC BY 4.0 (arXiv)](http://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2403.04642) · [PDF](https://arxiv.org/pdf/2403.04642) · [DOI 10.48550/arxiv.2403.04642](https://doi.org/10.48550/arxiv.2403.04642) · [arXiv 2403.04642](https://arxiv.org/abs/2403.04642) · [OpenAlex](https://openalex.org/W4392617563)

**Citations:** 3 citations (OpenAlex, 2026-10-14) · [58](https://md.research.elamur.ai/free/en/papers/havrilla-2024-teaching-large-language-models-reason/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
This study asks whether reinforcement learning techniques, popularised by RLHF, can strengthen the reasoning of large language models on math word problems. The authors compare three feedback-driven algorithms: Expert Iteration (EI), Proximal Policy Optimization (PPO) and Return-Conditioned RL (RCRL). They test them with several reward types: a sparse correctness reward, dense step-matching rewards and rewards from a learned Outcome-Based Reward Model (ORM). Experiments use 7B and 13B models, starting either from pretrained or supervised fine-tuned (SFT) checkpoints.

The simplest method, EI, usually comes out on top, and it needs roughly as many samples as PPO to converge. Unlike SFT, RL raises greedy accuracy and multi-sample coverage together, because it keeps producing fresh, varied training data. However, RL rarely finds solutions beyond what lightly fine-tuned models already reach. The authors attribute this to weak exploration and to the deterministic nature of reasoning tasks. They argue that better exploration is key to further progress and consider what this means for RLHF.

## Key points
- Four evaluation metrics are used: maj@1, maj@96, rerank@96 (answer chosen by an ORM) and pass@96. GSM8K is a central benchmark.
- Both EI and PPO converge after only about 60,000 rollouts, even from pretrained checkpoints. After RL, the pretrained-vs-SFT gap on GSM8K falls below 10%.
- Neither ORM guidance nor denser rewards gives a notable improvement over the plain sparse correctness reward.
- Llama-2-7B fine-tuned for 2 epochs (SFT 2) scores pass@96 of 0.76, versus 0.72 for 4 epochs (SFT 2's counterpart, SFT 4). SFT 2 also yields more unique correct solutions per train prompt (3.7 vs 2.9). With PPO, SFT 2's maj@1 rises from 0.36 to 0.43.
- PPO's KL penalty and clipped objective may explain why it beats EI in RLHF, where reward models are unreliable, but not on reasoning tasks with ground-truth rewards.

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

## Institutions

- [University of California, Berkeley](https://md.research.elamur.ai/free/en/universities/university-of-california-berkeley/) — University, Berkeley, United States · 209 works · 244,782 citations
- [Georgia Institute of Technology](https://md.research.elamur.ai/free/en/universities/georgia-institute-of-technology/) — University, Atlanta, United States · 152 works · 27,763 citations

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🧭 Topics (2): [🧠 Language models & pretraining](https://md.research.elamur.ai/free/en/topics/language-models/) · 3,894 works · [🧮 Reasoning](https://md.research.elamur.ai/free/en/topics/reasoning/) · 1,685 works

## Cite

Cite as: Alex Havrilla, Yuqing Du, Sharath Chandra Raparthy, Christoforos Nalmpantis, Jane Dwivedi-Yu, Maksym Zhuravinskyi, Eric Hambro, Sainbayar Sukhbaatar and Roberta Raileanu. 2024. Teaching Large Language Models to Reason with Reinforcement Learning. arXiv:2403.04642.

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

```bibtex
@misc{havrilla2024teaching,
  title = {{Teaching Large Language Models to Reason with Reinforcement Learning}},
  author = {Alex Havrilla, Yuqing Du, Sharath Chandra Raparthy, Christoforos Nalmpantis, Jane Dwivedi-Yu, Maksym Zhuravinskyi, Eric Hambro, Sainbayar Sukhbaatar and Roberta Raileanu},
  year = {2024},
  doi = {10.48550/arxiv.2403.04642},
  eprint = {2403.04642},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2403.04642}
}
```

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*Updated 2 November 2026*