What If Consensus Lies? Selective-Complementary Reinforcement Learning at Test Time

Test-time reinforcement learning (TTRL) improves the reasoning capabilities of large language models without labeled data by updating the policy with pseudo-labels constructed through majority voting. While effective, the reward signal assigned from majority voting is highly sensitive to consensus strength, defined as the frequency of the most common answer within a rollout group. In TTRL, consensus strength plays a dual role: it reflects both the reliability of the pseudo-label and the distribution of advantages. Low consensus can amplify updates from unreliable pseudo-labels through disproportionately large advantages, whereas high consensus reduces reward contrast and ultimately yields vanishing gradients. In this paper, we introduce Hi-TTRL, a test-time reinforcement learning framework that utilizes hints during sampling to regulate rollout consensus strength. Hi-TTRL first estimates consensus strength from a partial rollout group. When the consensus strength falls outside a target interval, it invokes a Markov chain Monte Carlo (MCMC) hint sampler. The sampler targets the power-transformed prefix distribution and uses finite-step approximate sampling to generate rollout prefixes as hints. By tuning the power exponent, Hi-TTRL generates hints with a sharpened or flattened power target, steering rollout consensus strength toward the target interval. Experiments on multiple datasets and backbones show that Hi-TTRL consistently improves over standard TTRL, with ablations and consensus-steering analyses validating the effectiveness of adaptive hint-guided consensus regulation.

Test-time reinforcement learning has emerged as a promising paradigm for enhancing the complex reasoning abilities of large language models in a completely label-free manner. Despite existing studies focusing on Pass@1 performance, optimizing Pass@k remains under-explored yet critical in label-free settings, which measures generation coverage for sustained exploration. Optimizing Pass@k in label-free setting is highly non-trivial, as directly applying the Pass@k advantage designs effective for RLVR yields unsatisfactory performance. Through in-depth empirical analysis, we discover the root causes hindering performance: pseudo-label estimations for low-confidence samples have a high probability of being incorrect, while candidate answers for high-confidence samples suffer from severe diversity collapse. To overcome these hurdles, we propose TTRL-CoCoV (Test-Time Reinforcement Learning with Confidence-Conditioned Verification), a novel confidence-adaptive framework that expands Pass@k coverage and improves Pass@1 performance. Based on our key insight that verification capability generally leads generation capability, TTRL-CoCoV employs a confidence-conditioned mechanism: for high-confidence samples, it bootstraps verifier and applies an exploration-enhancing reward to prevent diversity collapse; for low-confidence samples, it delegates pseudo-label selection to the verifier to filter incorrect pseudo-labels; and for medium-confidence samples, it bypasses verification entirely. Extensive experiments demonstrate that TTRL-CoCoV outperforms the best competing methods across 6 widely-recognized benchmarks, achieves average absolute gains of +9.8% in Pass@1 and +18.7% in Pass@16 over TTRL, and even achieves absolute Pass@1 improvements of up to +5.0% across multiple reasoning benchmarks when compared against fully supervised RL methods. Our code repository: https://github.com/shanjf666/CoCoV.

Current label-free RLVR approaches for large language models (LLMs), such as TTRL and Self-reward, have demonstrated effectiveness in improving the performance of LLMs on complex reasoning tasks. However, these methods rely heavily on accurate pseudo-label estimation and converge on spurious yet popular answers, thereby trapping in a dominant mode and limiting further improvements. Building on this, we propose Dual Consensus Reinforcement Learning (DCRL), a novel self-supervised training method which is capable of generating more reliable learning signals through a two-stage consensus mechanism. The model initially acts as an anchor, producing dominant responses; then it serves as an explorer, generating diverse auxiliary signals via a temporary unlearning process. The final training target is derived from the harmonic mean of these two signal sets. Notably, the process operates entirely without external models or supervision. Across eight benchmarks and diverse domains, DCRL consistently improves Pass@1 over majority vote while yielding more stable training dynamics. These results demonstrate that DCRL establishes a scalable path toward stronger reasoning without labels.