# Rethinking KL Regularization in RLHF: From Value Estimation to Gradient Optimization

arXiv: https://arxiv.org/abs/2510.01555 · HTML: https://mlsanity.com/paper/2510.01555/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Reward modeling and RLHF, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 17 of its 24 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Reward modeling and RLHF](https://mlsanity.com/alignment/reward-modeling-and-rlhf/)

## Builds on (most cited first, 17 of 17)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [Way Off-Policy Batch Deep Reinforcement Learning of Implicit Human Preferences in Dialog](https://mlsanity.com/paper/1907.00456/) (2019)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [MiniMax-01: Scaling Foundation Models with Lightning Attention](https://mlsanity.com/paper/2501.08313/) (2025)
- [Reinforcement Learning Optimization for Large-Scale Learning: An Efficient and User-Friendly Scaling Library](https://mlsanity.com/paper/2506.06122/) (2025)

## Built on by (most cited first, 14 of 14)

- [Skill-SD: Skill-Conditioned Self-Distillation for Multi-turn LLM Agents](https://mlsanity.com/paper/2604.10674/) (2026)
- [GenEvolve: Self-Evolving Image Generation Agents via Tool-Orchestrated Visual Experience Distillation](https://mlsanity.com/paper/2605.21605/) (2026)
- [Entropy-Preserving Supervised Fine-Tuning via Adaptive Self-Distillation for Large Reasoning Models](https://mlsanity.com/paper/2602.02244/) (2026)
- [Towards Robust LLM Post-Training: Automatic Failure Management for Reinforcement Fine-Tuning](https://mlsanity.com/paper/2605.04431/) (2026)
- [The Effectiveness of Approximate Regularized Replay for Efficient Supervised Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2512.22337/) (2025)
- [SWE-Fuse: Empowering Software Agents via Issue-free Trajectory Learning and Entropy-aware RLVR Training](https://mlsanity.com/paper/2603.07927/) (2026)
- [Advantage Scale Calibration Imbalance in Group-Relative Optimization under Low-Variance Rewards: Diagnosis and Bounded Recovery](https://mlsanity.com/paper/2609.19164/) (2026)
- [Unifying Adversarial Robustness and Training Across Text Scoring Models](https://mlsanity.com/paper/2602.00857/) (2026)
- [A Unified Framework for Rethinking Policy Divergence Measures in GRPO](https://mlsanity.com/paper/2602.05494/) (2026)
- [Generalisation of RLHF under Reward Shift and Clipped KL Regularisation](https://mlsanity.com/paper/2602.21765/) (2026)
- [TRIAGE: Dialectical Reasoning for Explainable Risk Prediction on Irregularly Sampled Medical Time Series with LLMs](https://mlsanity.com/paper/2606.09030/) (2026)
- [KLip-PPO: A per-sample KL perspective on PPO-Clip](https://mlsanity.com/paper/2606.23932/) (2026)
- [Suan: Rectifying Direct Preference Safety Alignment in Large Language Models](https://mlsanity.com/paper/2609.08634/) (2026)
- [One to More, More to One: Category-Aware Iterative Expert Training for Software Engineering Agents](https://mlsanity.com/paper/2609.23377/) (2026)

## Abstract (arXiv)

Reinforcement Learning from Human Feedback (RLHF) leverages a Kullback-Leibler (KL) divergence loss to stabilize training and prevent overfitting. However, in methods such as GRPO, its implementation may be guided by principles from numerical value estimation-a practice that overlooks the term's functional role as an optimization loss. To analyze this issue, we establish a unified framework that connects two seemingly distinct implementation styles: using the mathematical term kn as a detached coefficient for the policy's score function ('kn in reward') or as a direct loss function through which gradients are propagated ('kn as loss'). We show that the latter can always be analyzed via an equivalent gradient coefficient in the former, unifying the two perspectives. Through this framework, we prove that the conventional 'k1 in reward' (like in PPO) is the principled loss for Reverse KL (RKL) regularization. We further establish a key finding: under on-policy conditions, the 'k2 as loss' formulation is, in fact, gradient-equivalent to 'k1 in reward'. This equivalence, first proven in our work, identifies both as the theoretically sound implementations of the RKL objective. In contrast, we show that the recently adopted 'k3 as loss' (like in GRPO) is merely a first-order, biased approximation of the principled loss. Furthermore, we argue that common off-policy implementations of 'kn as loss' methods are biased due to neglected importance sampling, and we propose a principled correction. Our findings provide a comprehensive, gradient-based rationale for choosing and correctly implementing KL regularization, paving the way for more robust and effective RLHF systems.