Learn More with Less: Uncertainty Consistency Guided Query Selection for RLVR

Large Language Models (LLMs) have recently improved mathematical reasoning through Reinforcement Learning with Verifiable Reward (RLVR). However, existing RLVR algorithms require large query budgets, making annotation costly. We investigate whether fewer but more informative queries can yield similar or superior performance, introducing active learning (AL) into RLVR. We identify that classic AL sampling strategies fail to outperform random selection in this setting, due to ignoring \textbf{objective uncertainty} when only selecting by subjective uncertainty. This work proposes an \textbf{uncertainty consistency} metric to evaluate how well subjective uncertainty aligns with objective uncertainty. In the offline setting, this alignment is measured using the Point-Biserial Correlation Coefficient (PBC). For online training, because of limited sampling and dynamically shifting output distributions, PBC estimation is difficult. Therefore, we introduce a new online variant, computed from normalized advantage and subjective uncertainty. Theoretically, we prove that the online variant is strictly negatively correlated with offline PBC and supports better sample selection. Experiments show our method consistently outperforms random and classic AL baselines, achieving full-dataset performance while training on only 30\% of the data, effectively reducing the cost of RLVR for reasoning tasks.\footnote{The code is available at \hyperref[https://github.com/yihao-123/uncertainty-consistency]{https://github.com/yihao-123/uncertainty-consistency}. }