# Incentivizing Agentic Reasoning in LLM Judges via Tool-Integrated Reinforcement Learning

arXiv: https://arxiv.org/abs/2510.23038 · HTML: https://mlsanity.com/paper/2510.23038/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 80 of its 86 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)

## Builds on (most cited first, 30 of 80)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [Safe RLHF: Safe Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2310.12773/) (2023)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [BigCodeBench: Benchmarking Code Generation with Diverse Function Calls and Complex Instructions](https://mlsanity.com/paper/2406.15877/) (2024)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [ReTool: Reinforcement Learning for Strategic Tool Use in LLMs](https://mlsanity.com/paper/2504.11536/) (2025)
- [Interpretable Preferences via Multi-Objective Reward Modeling and Mixture-of-Experts](https://mlsanity.com/paper/2406.12845/) (2024)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [R1-Searcher: Incentivizing the Search Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2503.05592/) (2025)
- [Skywork-Reward: Bag of Tricks for Reward Modeling in LLMs](https://mlsanity.com/paper/2410.18451/) (2024)
- [JudgeBench: A Benchmark for Evaluating LLM-based Judges](https://mlsanity.com/paper/2410.12784/) (2024)
- [WebRL: Training LLM Web Agents via Self-Evolving Online Curriculum Reinforcement Learning](https://mlsanity.com/paper/2411.02337/) (2024)

## Built on by (most cited first, 17 of 17)

- [Alternating Reinforcement Learning for Rubric-Based Reward Modeling in Non-Verifiable LLM Post-Training](https://mlsanity.com/paper/2602.01511/) (2026)
- [Agent0-VL: Exploring Self-Evolving Agent for Tool-Integrated Vision-Language Reasoning](https://mlsanity.com/paper/2511.19900/) (2025)
- [Scaling Agentic Reinforcement Learning for Tool-Integrated Reasoning in VLMs](https://mlsanity.com/paper/2511.19773/) (2025)
- [Agent-as-a-Judge](https://mlsanity.com/paper/2601.05111/) (2026)
- [AgentV-RL: Scaling Reward Modeling with Agentic Verifier](https://mlsanity.com/paper/2604.16004/) (2026)
- [AJ-Bench: Benchmarking Agent-as-a-Judge for Environment-Aware Evaluation](https://mlsanity.com/paper/2604.18240/) (2026)
- [More Convincing, Not More Correct: Self-Play Reward Hacking of Reference-Free LLM Judges](https://mlsanity.com/paper/2607.05904/) (2026)
- [ToolRM: Towards Agentic Tool-Use Reward Modeling](https://mlsanity.com/paper/2510.26167/) (2025)
- [RUBRIC-ARROW: Alternating Pointwise Rubric Reward Modeling for LLM Post-training in Non-verifiable Domains](https://mlsanity.com/paper/2605.29156/) (2026)
- [Scaling Medical Reasoning Verification via Tool-Integrated Reinforcement Learning](https://mlsanity.com/paper/2601.20221/) (2026)
- [Skill-RM: Unifying Heterogeneous Evaluation Criteria via Agent Skill](https://mlsanity.com/paper/2606.03980/) (2026)
- [CE-RM: A Pointwise Generative Reward Model Optimized via Two-Stage Rollout and Unified Criteria](https://mlsanity.com/paper/2601.20327/) (2026)
- [Evaluating Agentic Configuration Repair for Computer Networks](https://mlsanity.com/paper/2606.06212/) (2026)
- [IRPM: Intergroup Relative Preference Modeling for Pointwise Generative Reward Models](https://mlsanity.com/paper/2601.00677/) (2026)
- [Tool-Aware Optimization with Entropy Guidance for Efficient Agentic Reinforcement Learning](https://mlsanity.com/paper/2606.03762/) (2026)
- [WMLLM: Self-Evolving Optimization Agents via Predict-Then-Act World Modeling](https://mlsanity.com/paper/2609.01608/) (2026)
- [Rubrics from the Task, Verdicts from Evidence: Pointwise Rubric Rewards with Tool-Augmented Judges](https://mlsanity.com/paper/2610.18766/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) are widely used as judges to evaluate response quality, providing a scalable alternative to human evaluation. However, most LLM judges operate solely on intrinsic text-based reasoning, limiting their ability to verify complex constraints or perform accurate computation. Motivated by the success of tool-integrated reasoning (TIR) in numerous tasks, we propose TIR-Judge, an end-to-end RL framework for training LLM judges that integrates a code executor for precise evaluation. TIR-Judge is built on three principles: (i) diverse training across verifiable and non-verifiable domains, (ii) flexible judgment formats (pointwise, pairwise, listwise), and (iii) iterative RL that bootstraps directly from the initial model without distillation. On seven public benchmarks, TIR-Judge surpasses strong reasoning-based judges by up to 6.4% (pointwise) and 7.7% (pairwise), and achieves listwise performance comparable to Claude-Opus-4 despite having only 8B parameters. Remarkably, TIR-Judge-Zero - trained entirely without distilled judge trajectories, matches the performance of distilled variants, demonstrating that tool-augmented judges can self-evolve through iterative reinforcement learning.