# REAL: Regression-Aware Reinforcement Learning for LLM-as-a-Judge

arXiv: https://arxiv.org/abs/2603.17145 · HTML: https://mlsanity.com/paper/2603.17145/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 17 Mar 2026.

## Builds on (most cited first, 30 of 31)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [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)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [A General Language Assistant as a Laboratory for Alignment](https://mlsanity.com/paper/2112.00861/) (2021)
- [Can Large Language Models Be an Alternative to Human Evaluations?](https://mlsanity.com/paper/2305.01937/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (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)
- [Prometheus 2: An Open Source Language Model Specialized in Evaluating Other Language Models](https://mlsanity.com/paper/2405.01535/) (2024)
- [JudgeLM: Fine-tuned Large Language Models are Scalable Judges](https://mlsanity.com/paper/2310.17631/) (2023)
- [PandaLM: An Automatic Evaluation Benchmark for LLM Instruction Tuning Optimization](https://mlsanity.com/paper/2306.05087/) (2023)
- [Reinforcement learning](https://mlsanity.com/paper/2405.10369/) (2024)
- [Generative Judge for Evaluating Alignment](https://mlsanity.com/paper/2310.05470/) (2023)
- [Gradient Estimation Using Stochastic Computation Graphs](https://mlsanity.com/paper/1506.05254/) (2015)
- [Not All Rollouts are Useful: Down-Sampling Rollouts in LLM Reinforcement Learning](https://mlsanity.com/paper/2504.13818/) (2025)
- [J1: Incentivizing Thinking in LLM-as-a-Judge via Reinforcement Learning](https://mlsanity.com/paper/2505.10320/) (2025)
- [Reinforcement Learning for Bandit Neural Machine Translation with Simulated Human Feedback](https://mlsanity.com/paper/1707.07402/) (2017)
- [Beyond Verifiable Rewards: Scaling Reinforcement Learning for Language Models to Unverifiable Data](https://mlsanity.com/paper/2503.19618/) (2025)
- [TRACT: Regression-Aware Fine-tuning Meets Chain-of-Thought Reasoning for LLM-as-a-Judge](https://mlsanity.com/paper/2503.04381/) (2025)
- [Regression-aware Inference with LLMs](https://mlsanity.com/paper/2403.04182/) (2024)

## Built on by (most cited first, 2 of 2)

- [CACSurv: Concordance-Aligned Comparative Learning with Large Language Models for Cancer Survival Prediction](https://mlsanity.com/paper/2608.16594/) (2026)
- [DUALVIEW: Leveraging Broad and Output-Specific Evidence for LLM-based Multi-Output Text Regression](https://mlsanity.com/paper/2610.19206/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are increasingly deployed as automated evaluators that assign numeric scores to model outputs, a paradigm known as LLM-as-a-Judge. However, standard Reinforcement Learning (RL) methods typically rely on binary rewards (e.g., 0-1 accuracy), thereby ignoring the ordinal structure inherent in regression tasks; for instance, they fail to recognize that predicting 4 is significantly better than predicting 1 when the ground truth is 5. Conversely, existing regression-aware approaches are often confined to Supervised Fine-Tuning (SFT), limiting their ability to explore optimal reasoning paths. To bridge this gap, we propose REAL (underlineREgression-underlineAware Reinforcement underlineLearning), a principled RL framework designed to optimize regression rewards, and also proven to be optimal for correlation metrics. A key technical challenge is that the regression objective is explicitly policy-dependent, thus invalidating standard policy gradient methods. To address this, we employ the generalized policy gradient estimator, which naturally decomposes optimization into two complementary components: (1) exploration over Chain-of-Thought (CoT) trajectory, and (2) regression-aware prediction refinement of the final score. Extensive experiments across model scales (8B to 32B) demonstrate that REAL consistently outperforms both regression-aware SFT baselines and standard RL methods, exhibiting significantly better generalization on out-of-domain benchmarks. On Qwen3-32B specifically, we achieve gains of +8.40 Pearson and +7.20 Spearman correlation over the SFT baseline, and +18.30/+11.20 over the base model. These findings highlight the critical value of integrating regression objectives into RL exploration for accurate LLM evaluation.