TraPO: A Semi-Supervised Reinforcement Learning Framework for Boosting LLM Reasoning

TL;DR

TraPO introduces a semi-supervised reinforcement learning framework that significantly improves reasoning model performance by effectively leveraging limited labeled data alongside unlabeled data, achieving high accuracy with less supervision.

Contribution

The paper proposes TraPO, a novel semi-supervised RLVR method that stabilizes training using a small labeled set, enhancing data efficiency and outperformance of fully supervised models.

Findings

TraPO achieves 42.6% accuracy with only 1K labeled and 3K unlabeled samples.

It surpasses unsupervised methods trained on much larger unlabeled datasets.

With 4K labeled and 12K unlabeled samples, TraPO outperforms fully supervised models.

Abstract

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.