# Reasoning Arena: Trace Tournaments When Verifiable Rewards Fall Short

arXiv: https://arxiv.org/abs/2606.09380 · HTML: https://mlsanity.com/paper/2606.09380/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 18 of 18)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [DR Tulu: Reinforcement Learning with Evolving Rubrics for Deep Research](https://mlsanity.com/paper/2511.19399/) (2025)
- [Ministral 3](https://mlsanity.com/paper/2601.08584/) (2026)
- [DeepSeekMath-V2: Towards Self-Verifiable Mathematical Reasoning](https://mlsanity.com/paper/2511.22570/) (2025)
- [Pref-GRPO: Pairwise Preference Reward-based GRPO for Stable Text-to-Image Reinforcement Learning](https://mlsanity.com/paper/2508.20751/) (2025)
- [RLPR: Extrapolating RLVR to General Domains without Verifiers](https://mlsanity.com/paper/2506.18254/) (2025)
- [Online Rubrics Elicitation from Pairwise Comparisons](https://mlsanity.com/paper/2510.07284/) (2025)
- [VISTA: A Test-Time Self-Improving Video Generation Agent](https://mlsanity.com/paper/2510.15831/) (2025)
- [Open Rubric System: Scaling Reinforcement Learning with Pairwise Adaptive Rubric](https://mlsanity.com/paper/2602.14069/) (2026)
- [Towards High Data Efficiency in Reinforcement Learning with Verifiable Reward](https://mlsanity.com/paper/2509.01321/) (2025)
- [Maestro: Self-Improving Text-to-Image Generation via Agent Orchestration](https://mlsanity.com/paper/2509.10704/) (2025)
- [ArenaRL: Scaling RL for Open-Ended Agents via Tournament-based Relative Ranking](https://mlsanity.com/paper/2601.06487/) (2026)
- [Examining Reasoning LLMs-as-Judges in Non-Verifiable LLM Post-Training](https://mlsanity.com/paper/2603.12246/) (2026)

## Abstract (arXiv)

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.