# RLVR2: Reinforcement Learning with Verifiable Rubric-based Ranking

arXiv: https://arxiv.org/abs/2609.23457 · HTML: https://mlsanity.com/paper/2609.23457/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 47 of its 53 references that are in the map.
- First posted on arXiv 20 Sep 2026.

## Builds on (most cited first, 30 of 47)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Prometheus: Inducing Fine-grained Evaluation Capability in Language Models](https://mlsanity.com/paper/2310.08491/) (2023)
- [From Crowdsourced Data to High-Quality Benchmarks: Arena-Hard and BenchBuilder Pipeline](https://mlsanity.com/paper/2406.11939/) (2024)
- [GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models](https://mlsanity.com/paper/2508.06471/) (2025)
- [HealthBench: Evaluating Large Language Models Towards Improved Human Health](https://mlsanity.com/paper/2505.08775/) (2025)
- [LongBench v2: Towards Deeper Understanding and Reasoning on Realistic Long-context Multitasks](https://mlsanity.com/paper/2412.15204/) (2024)
- [Rubrics as Rewards: Reinforcement Learning Beyond Verifiable Domains](https://mlsanity.com/paper/2507.17746/) (2025)
- [PaperBench: Evaluating AI's Ability to Replicate AI Research](https://mlsanity.com/paper/2504.01848/) (2025)
- [Generalizing Verifiable Instruction Following](https://mlsanity.com/paper/2507.02833/) (2025)
- [GDPO: Group reward-Decoupled Normalization Policy Optimization for Multi-reward RL Optimization](https://mlsanity.com/paper/2601.05242/) (2026)
- [MultiChallenge: A Realistic Multi-Turn Conversation Evaluation Benchmark Challenging to Frontier LLMs](https://mlsanity.com/paper/2501.17399/) (2025)
- [Fact, Fetch, and Reason: A Unified Evaluation of Retrieval-Augmented Generation](https://mlsanity.com/paper/2409.12941/) (2024)
- [OpenRubrics: Towards Scalable Synthetic Rubric Generation for Reward Modeling and LLM Alignment](https://mlsanity.com/paper/2510.07743/) (2025)
- [Checklists Are Better Than Reward Models For Aligning Language Models](https://mlsanity.com/paper/2507.18624/) (2025)
- [Reinforcement Learning with Rubric Anchors](https://mlsanity.com/paper/2508.12790/) (2025)
- [Reward Shaping to Mitigate Reward Hacking in RLHF](https://mlsanity.com/paper/2502.18770/) (2025)
- [EQ-Bench: An Emotional Intelligence Benchmark for Large Language Models](https://mlsanity.com/paper/2312.06281/) (2023)
- [Breaking the Exploration Bottleneck: Rubric-Scaffolded Reinforcement Learning for General LLM Reasoning](https://mlsanity.com/paper/2508.16949/) (2025)
- [SimpleQA Verified: A Reliable Factuality Benchmark to Measure Parametric Knowledge](https://mlsanity.com/paper/2509.07968/) (2025)
- [RubricHub: A Comprehensive and Highly Discriminative Rubric Dataset via Automated Coarse-to-Fine Generation](https://mlsanity.com/paper/2601.08430/) (2026)
- [AdvancedIF: Rubric-Based Benchmarking and Reinforcement Learning for Advancing LLM Instruction Following](https://mlsanity.com/paper/2511.10507/) (2025)
- [Rethinking Bradley-Terry Models in Preference-Based Reward Modeling: Foundations, Theory, and Alternatives](https://mlsanity.com/paper/2411.04991/) (2024)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) is expanding from tasks with well-defined correctness signals, such as mathematics and code, toward multifaceted quality requirements specified by multi-dimensional rubrics. Since policy optimization consumes one scalar per rollout, rubric-based pipelines must map multiple criterion scores into a scalar reward. This aggregation is often treated as score scaling, but it implicitly determines how quality dimensions trade off during training. The prevailing practice, normalizing each criterion and taking a linear combination, assumes that cardinal score differences are comparable across criteria and that gains on one criterion compensate for failures on another; both assumptions are unreliable when criteria are semantically heterogeneous. We propose Reinforcement Learning with Verifiable Rubric-based Ranking (RLVR2), a verifiable ranking paradigm for rubric-based RLVR. For each criterion, RLVR2 converts rubric scores into criterion-specific within-group ordinal outcomes, recovers a latent utility from the resulting comparison matrix, and merges these utilities into one training signal. By retaining only within-group ordering and discarding raw score magnitudes, RLVR2 avoids calibrating heterogeneous rubric scales. It further supports objective-preserving attribute adjustment: auxiliary attributes that correlate with observed rankings but are not training objectives can enter the estimation without expanding the rubric or rewarding them directly. Across three model scales and 16 benchmarks, RLVR2 consistently outperforms representative rubric-based baselines, achieving the best overall performance on most benchmarks at every scale. Analysis shows it controls systematic effects tied to reasoning efficiency and response formatting while preserving the quality objective.