OREAL
Exploring the Limit of Outcome Reward for Learning Mathematical Reasoning
Stars: 96
OREAL is a reinforcement learning framework designed for mathematical reasoning tasks, aiming to achieve optimal performance through outcome reward-based learning. The framework utilizes behavior cloning, reshaping rewards, and token-level reward models to address challenges in sparse rewards and partial correctness. OREAL has achieved significant results, with a 7B model reaching 94.0 pass@1 accuracy on MATH-500 and surpassing previous 32B models. The tool provides training tutorials and Hugging Face model repositories for easy access and implementation.
README:
Reasoning abilities, especially those for solving complex math problems, are crucial components of general intelligence. Recent advances by proprietary companies, such as o-series models of OpenAI, have made remarkable progress on reasoning tasks. However, the complete technical details remain unrevealed, and the techniques that are believed certainly to be adopted are only reinforcement learning (RL) and the long chain of thoughts.
We proposes a new RL framework, termed OREAL, to pursue the performance limit that can be achieved through Outcome REwArd-based reinforcement Learning for mathematical reasoning tasks, where only binary outcome rewards are easily accessible.
- We theoretically prove that behavior cloning on positive trajectories from best-of-N (BoN) sampling is sufficient to learn the KL-regularized optimal policy in binary feedback environments.
- This formulation further implies that the rewards of negative samples should be reshaped to ensure the gradient consistency between positive and negative samples.
- To alleviate the long-existing difficulties brought by sparse rewards in RL, which are even exacerbated by the partial correctness of the long chain of thought for reasoning tasks, we further apply a token-level reward model to sample important tokens in reasoning trajectories for learning.
The OREAL implementation pseudocode is as follows:
With OREAL, for the first time, a 7B model can obtain 94.0 pass@1 accuracy on MATH-500 through RL, being on par with 32B models. OREAL-32B also surpasses previous 32B models trained by distillation with 95.0 pass@1 accuracy on MATH-500.
Our OREAL models are available on Hugging Face 🤗:
| Model | Huggingface Repo |
|---|---|
| OREAL-7B | Model Link |
| OREAL-32B | Model Link |
We also release the models of SFT version. You can construct your own RL pipeline on them:)
| Model | Huggingface Repo |
|---|---|
| OREAL-7B-SFT | Model Link |
| OREAL-32B-SFT | Model Link |
OREAL utilizes XTuner as the training engine.
pip install torch==2.5.1 torchvision==0.20.1 torchaudio==2.5.1 --index-url https://download.pytorch.org/whl/cu124
pip install flash-attn --no-build-isolation
pip install -r requirements.txtThe training data can be found at HERE. The training script will automatically download the data from huggingface.
OREAL requires a language model as a verifier to evaluate the correctness of the generated solutions along with a rule based verificy function (see the source code). We use Qwen2.5-72B-Instruct as the verifier in our experiments. You can start the verifier service with lmdeploy by running the following command:
lmdeploy serve api_server Qwen/Qwen2.5-72B-Instruct --tp 4 --chat-template qwen --log-level INFO --server-port 10003Or you can use any other inference engine such as sglang or vllm or ollama. Just make sure the verifier service can be reached by OpenAI-compatible API.
Fill in the verifier service address in the config file before training.
judgers_config = dict(
math_judger=dict( # math judger related settings
hosts=["x.x.x.x:xxxx", "x.x.x.x:xxxx"], # verifier service addresses
stop_word=stop_word,
thinking_finish_words=["<conclude>", "**Final Answer**", "</think>"],
num_processes=8,
concurrency_per_proc=(8, 8),
)
)OREAL-7B
7B requires 32 GPUs to train. You can use the following command to train the model with OREAL-7B-SFT as the initial policy:
torchrun --nnodes 4 --nproc_per_node 8 --master_addr $MASTER_ADDR --node_rank $RANK --master_port $MASTER_PORT train_oreal.py oreal/configs/oreal_w_tokenrm_OREAL-7B-SFT_seqlen16k.py --total_steps 90 --work_dir ./work_dir/oreal_w_tokenrm_OREAL-7B-SFT_seqlen16kIt takes about 9 hours to train the model 90 steps with 32xA100.
OREAL-32B
32B requires 128 GPUs to train. You can use the following command to train the model with OREAL-32B-SFT as the initial policy:
torchrun --nnodes 16 --nproc_per_node 8 --master_addr $MASTER_ADDR --node_rank $RANK --master_port $MASTER_PORT train_oreal.py oreal/configs/oreal_w_tokenrm_OREAL-32B-SFT_seqlen16k.py --total_steps 90 --work_dir ./work_dir/oreal_w_tokenrm_OREAL-32B-SFT_seqlen16kMore detailed training settings can be found in the oreal/configs folder.
Note:
- The best checkpoint may not be the last one. Consider evaluating during training and early stopping when the performance is saturated.
@misc{lyu2025exploringlimitoutcomereward,
title={Exploring the Limit of Outcome Reward for Learning Mathematical Reasoning},
author={Chengqi Lyu and Songyang Gao and Yuzhe Gu and Wenwei Zhang and Jianfei Gao and Kuikun Liu and Ziyi Wang and Shuaibin Li and Qian Zhao and Haian Huang and Weihan Cao and Jiangning Liu and Hongwei Liu and Junnan Liu and Songyang Zhang and Dahua Lin and Kai Chen},
year={2025},
eprint={2502.06781},
archivePrefix={arXiv},
primaryClass={cs.CL},
url={https://arxiv.org/abs/2502.06781},
}
This project is released under the Apache 2.0 license.
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