Abstract

Test-time reinforcement learning mitigates the reliance on annotated data by using majority voting results as pseudo-labels, emerging as a complementary direction to reinforcement learning with verifiable rewards (RLVR) for improving reasoning ability of large language models (LLMs). However, this voting strategy often induces confirmation bias and suffers from sparse rewards, limiting the overall performance. In this work, we propose subgroup-specific step-wise confidence-weighted pseudo-label estimation (SCOPE), a framework integrating model confidence and dynamic subgroup partitioning to address these issues. Specifically, SCOPE integrates the proposed step-wise confidence into pseudo-label estimation, prioritizing high-quality reasoning paths over simple frequency count. Furthermore, it dynamically partitions the candidate outputs pool into independent subgroups by balancing reasoning quality against exploration diversity. By deriving local consensus via repeat sampling for each subgroup, SCOPE provides diverse supervision targets to encourage broader exploration. We conduct experiments across various models and benchmarks, experimental results show that SCOPE consistently outperforms recent baselines. Notably, SCOPE achieves relative improvements of 13.1% on challenging AIME 2025 and 8.1% on AMC.