TraPO: A Semi-Supervised Reinforcement Learning Framework for Boosting LLM Reasoning
Reinforcement learning with verifiable rewards (RLVR) has proven effective in training large reasoning models (LRMs) by leveraging answer-verifiable signals to guide policy optimization, which, however, suffers from high annotation costs. To alleviate this problem, recent work has explored unsupervised RLVR methods that derive rewards solely from the model's internal consistency, such as through entropy and majority voting. While seemingly promising, these methods often suffer from model collapse in the later stages of training, which may arise from the reinforcement of incorrect reasoning patterns in the absence of external supervision. In this work, we investigate a novel semi-supervised RLVR paradigm that utilizes a small labeled set to guide RLVR training on unlabeled samples. Our key insight is that supervised rewards are essential for stabilizing consistency-based training on unlabeled samples, ensuring that only reasoning patterns verified on labeled instances are incorporated into RL training. Technically, we propose an effective policy optimization algorithm, TraPO, that identifies reliable unlabeled samples by matching their learning trajectory similarity to labeled ones. Building on this, TraPO achieves remarkable data efficiency and strong generalization on six widely used mathematical reasoning benchmarks (AIME24/25, AMC, MATH-500, Minerva, and Olympiad) and three out-of-distribution tasks (ARC-c, GPQA-diamond, and MMLU-pro). With only 1K labeled and 3K unlabeled samples, TraPO reaches 42.6% average accuracy, surpassing the best unsupervised method trained on 45K unlabeled samples (38.3%). Notably, when using 4K labeled and 12K unlabeled samples, TraPO even outperforms the fully supervised model trained on the full 45K labeled samples on all benchmarks, while using only 10% of the labeled data. The code is available via https://github.com/ShenzhiYang2000/TRAPO.
69423a805d5b2dc105274902
Shenzhi Yang
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2025-12-17T10:07:56.545Z
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Shenzhi Yang
Shenzhi
user
Shenzhi
69423a805d5b2dc105274903
Guangcheng Zhu
69423a805d5b2dc105274904
Xing Zheng
69423a805d5b2dc105274905
Yingfan MA
69423a805d5b2dc105274906
Zhongqi Chen
69423a805d5b2dc105274907
Bowen Song
69423a805d5b2dc105274908
Weiqiang Wang
69423a805d5b2dc105274909
Junbo Zhao
69423a805d5b2dc10527490a
Gang Chen
69423a805d5b2dc10527490b
Haobo Wang
TraPO: A Semi-Supervised Reinforcement Learning Framework for Boosting LLM Reasoning
Reinforcement learning with verifiable rewards (RLVR) has proven effective in training large reasoning models (LRMs) by leveraging answer-verifiable signals to guide policy optimization, which, however, suffers from high annotation costs. To alleviate this problem, recent work has explored unsupervised RLVR methods that derive rewards solely from the model's internal consistency, such as through entropy and majority voting. While seemingly promising, these methods often suffer from model collapse in the later stages of training, which may arise from the reinforcement of incorrect reasoning patterns in the absence of external supervision. In this work, we investigate a novel semi-supervised RLVR paradigm that utilizes a small labeled set to guide RLVR training on unlabeled samples. Our key insight is that supervised rewards are essential for stabilizing consistency-based training on unlabeled samples, ensuring that only reasoning patterns verified on labeled instances are incorporated into RL training. Technically, we propose an effective policy optimization algorithm, TraPO, that identifies reliable unlabeled samples by matching their learning trajectory similarity to labeled ones. Building on this, TraPO achieves remarkable data efficiency and strong generalization on six widely used mathematical reasoning benchmarks (AIME24/25, AMC, MATH-500, Minerva, and Olympiad) and three out-of-distribution tasks (ARC-c, GPQA-diamond, and MMLU-pro). With only 1K labeled and 3K unlabeled samples, TraPO reaches 42.6% average accuracy, surpassing the best unsupervised method trained on 45K unlabeled samples (38.3%). Notably, when using 4K labeled and 12K unlabeled samples, TraPO even outperforms the fully supervised model trained on the full 45K labeled samples on all benchmarks, while using only 10% of the labeled data. The code is available via https://github.com/ShenzhiYang2000/TRAPO.
A semi-supervised reinforcement learning with verifiable rewards approach uses a small labeled dataset to guide training on unlabeled samples, achieving high efficiency and accuracy in mathematical reasoning tasks.
reinforcement learning with verifiable rewards RLVR large reasoning models LRMs unsupervised RLVR entropy majority voting model collapse TraPO learning trajectory similarity AIME24/25 AMC MATH-500 Minerva Olympiad ARC-c GPQA-diamond MMLU-pro