Reasoning Arena: Trace Tournaments When Verifiable Rewards Fall Short
2026-06-08 • Machine Learning
Machine LearningArtificial IntelligenceComputation and Language
AI summaryⓘ
The authors address a problem in training language models where many examples get the same reward, making it hard for the model to learn which reasoning is better. They introduce Reasoning Arena, a system that compares reasoning steps within these same-reward groups to find subtle differences and create more detailed feedback. Instead of comparing every pair, they compare new examples to a small set of anchors to save time. Their tests show this approach improves reasoning performance and training speed compared to previous methods.
reinforcement learningverifiable rewardslanguage modelsreward estimationrelative rankingBradley-Terry modeltrace tournamentsgradient updatesreasoning performance
Authors
Han Zhou, Adam X. Yang, Laurence Aitchison, Anna Korhonen, Albert Q. Jiang
Abstract
Reinforcement learning with verifiable rewards (RLVR) has become a leading paradigm for improving the reasoning ability of large language models through outcome-based supervision. However, verifiable rewards frequently become uninformative at the group level: when all sampled traces of a given prompt receive identical rewards, group-relative advantage estimation provides no gradient signal, even though the traces may differ substantially in reasoning quality. We propose Reasoning Arena, an adaptive training framework that routes such non-diverse reward groups to a judge system instead of discarding them. Beyond examining the final answer, Reasoning Arena constructs trace tournaments, where reasoning traces are compared head-to-head to expose finer-grained preferences within the group, converting reasoning quality into rich relative reward signals. To make reward estimation efficient, rather than exhaustively comparing every pair, each new trace is evaluated against a small, dynamically updated pool of previously generated traces as anchors to efficiently establish a relative ranking. We then fit a Bradley-Terry model on the incomplete comparison graph, enabling scalable RL integration without quadratic pairwise comparisons. Empirical results demonstrate that Reasoning Arena consistently outperforms the RLVR baseline by 7.6% on average in competition mathematics and coding benchmarks. By converting otherwise wasted zero-advantage samples into useful gradient updates, our method accelerates training by 27% to 41%, saving nearly 50% of generation compute, and substantially improves overall reasoning performance.