# Correcting the Mythos of KL-Regularization: Direct Alignment without Overoptimization via Chi-Squared Preference Optimization

arXiv: https://arxiv.org/abs/2407.13399 · HTML: https://mlsanity.com/paper/2407.13399/

## Key facts

- Cited by 78 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 48 of its 103 references that are in the map.
- First posted on arXiv 18 Jul 2024.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 30 of 48)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [Statistical Rejection Sampling Improves Preference Optimization](https://mlsanity.com/paper/2309.06657/) (2023)
- [RLHF Workflow: From Reward Modeling to Online RLHF](https://mlsanity.com/paper/2405.07863/) (2024)
- [Direct Language Model Alignment from Online AI Feedback](https://mlsanity.com/paper/2402.04792/) (2024)
- [From r to Q^*: Your Language Model is Secretly a Q-Function](https://mlsanity.com/paper/2404.12358/) (2024)
- [Smaug: Fixing Failure Modes of Preference Optimisation with DPO-Positive](https://mlsanity.com/paper/2402.13228/) (2024)
- [Self-Play Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2405.00675/) (2024)
- [Reward Model Ensembles Help Mitigate Overoptimization](https://mlsanity.com/paper/2310.02743/) (2023)
- [Nash Learning from Human Feedback](https://mlsanity.com/paper/2312.00886/) (2023)
- [Helping or Herding? Reward Model Ensembles Mitigate but do not Eliminate Reward Hacking](https://mlsanity.com/paper/2312.09244/) (2023)
- [Advancing LLM Reasoning Generalists with Preference Trees](https://mlsanity.com/paper/2404.02078/) (2024)
- [Preference Fine-Tuning of LLMs Should Leverage Suboptimal, On-Policy Data](https://mlsanity.com/paper/2404.14367/) (2024)
- [Direct Nash Optimization: Teaching Language Models to Self-Improve with General Preferences](https://mlsanity.com/paper/2404.03715/) (2024)
- [Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints](https://mlsanity.com/paper/2309.16240/) (2023)
- [Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage](https://mlsanity.com/paper/2107.06226/) (2021)
- [Hybrid RL: Using Both Offline and Online Data Can Make RL Efficient](https://mlsanity.com/paper/2210.06718/) (2022)
- [Generalized Preference Optimization: A Unified Approach to Offline Alignment](https://mlsanity.com/paper/2402.05749/) (2024)
- [A Minimaximalist Approach to Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2401.04056/) (2024)
- [Scaling Laws for Reward Model Overoptimization in Direct Alignment Algorithms](https://mlsanity.com/paper/2406.02900/) (2024)
- [Provably Mitigating Overoptimization in RLHF: Your SFT Loss is Implicitly an Adversarial Regularizer](https://mlsanity.com/paper/2405.16436/) (2024)
- [Dueling RL: Reinforcement Learning with Trajectory Preferences](https://mlsanity.com/paper/2111.04850/) (2021)
- [Exploratory Preference Optimization: Harnessing Implicit Q*-Approximation for Sample-Efficient RLHF](https://mlsanity.com/paper/2405.21046/) (2024)
- [Is RLHF More Difficult than Standard RL?](https://mlsanity.com/paper/2306.14111/) (2023)
- [Confronting Reward Model Overoptimization with Constrained RLHF](https://mlsanity.com/paper/2310.04373/) (2023)

## Built on by (most cited first, 30 of 78)

- [Is Best-of-N the Best of Them? Coverage, Scaling, and Optimality in Inference-Time Alignment](https://mlsanity.com/paper/2503.21878/) (2025)
- [Scaling Test-Time Compute Without Verification or RL is Suboptimal](https://mlsanity.com/paper/2502.12118/) (2025)
- [Unintentional Unalignment: Likelihood Displacement in Direct Preference Optimization](https://mlsanity.com/paper/2410.08847/) (2024)
- [All Roads Lead to Likelihood: The Value of Reinforcement Learning in Fine-Tuning](https://mlsanity.com/paper/2503.01067/) (2025)
- [A Survey of Direct Preference Optimization](https://mlsanity.com/paper/2503.11701/) (2025)
- [Inference-Time Reward Hacking in Large Language Models](https://mlsanity.com/paper/2506.19248/) (2025)
- [Sharp Analysis for KL-Regularized Contextual Bandits and RLHF](https://mlsanity.com/paper/2411.04625/) (2024)
- [On a few pitfalls in KL divergence gradient estimation for RL](https://mlsanity.com/paper/2506.09477/) (2025)
- [Accelerating RL for LLM Reasoning with Optimal Advantage Regression](https://mlsanity.com/paper/2505.20686/) (2025)
- [Logarithmic Regret for Online KL-Regularized Reinforcement Learning](https://mlsanity.com/paper/2502.07460/) (2025)
- [Distortion of AI Alignment: Does Preference Optimization Optimize for Preferences?](https://mlsanity.com/paper/2505.23749/) (2025)
- [Robust LLM Alignment via Distributionally Robust Direct Preference Optimization](https://mlsanity.com/paper/2502.01930/) (2025)
- [Adaptive Rollout Allocation for Online Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2602.01601/) (2026)
- [Extragradient Preference Optimization (EGPO): Beyond Last-Iterate Convergence for Nash Learning from Human Feedback](https://mlsanity.com/paper/2503.08942/) (2025)
- [SpatialThinker: Reinforcing Scene Graph-Grounded Spatial Reasoning via Dense Rewards](https://mlsanity.com/paper/2511.07403/) (2025)
- [Sail into the Headwind: Alignment via Robust Rewards and Dynamic Labels against Reward Hacking](https://mlsanity.com/paper/2412.09544/) (2024)
- [Future-KL Regularized GRPO: Process-Level Credit Assignment from f-Divergence Regularization](https://mlsanity.com/paper/2601.10201/) (2026)
- [KL-Regularized RLHF with Multiple Reference Models: Exact Solutions and Sample Complexity](https://mlsanity.com/paper/2502.01203/) (2025)
- [Forward KL Regularized Preference Optimization for Aligning Diffusion Policies](https://mlsanity.com/paper/2409.05622/) (2024)
- [Towards a Sharp Analysis of Offline Policy Learning for f-Divergence-Regularized Contextual Bandits](https://mlsanity.com/paper/2502.06051/) (2025)
- [Offline Reinforcement Learning in Large State Spaces: Algorithms and Guarantees](https://mlsanity.com/paper/2510.04088/) (2025)
- [Faster WIND: Accelerating Iterative Best-of-N Distillation for LLM Alignment](https://mlsanity.com/paper/2410.20727/) (2024)
- [Preference Optimization by Estimating the Ratio of the Data Distribution](https://mlsanity.com/paper/2505.19601/) (2025)
- [Mitigating Preference Hacking in Policy Optimization with Pessimism](https://mlsanity.com/paper/2503.06810/) (2025)
- [A Unified Theoretical Analysis of Private and Robust Offline Alignment: from RLHF to DPO](https://mlsanity.com/paper/2505.15694/) (2025)
- [Diffusion-SDPO: Safeguarded Direct Preference Optimization for Diffusion Models](https://mlsanity.com/paper/2511.03317/) (2025)
- [RSPO: Regularized Self-Play Alignment of Large Language Models](https://mlsanity.com/paper/2503.00030/) (2025)
- [Learning a Pessimistic Reward Model in RLHF](https://mlsanity.com/paper/2505.20556/) (2025)
- [Information-Theoretic Reward Modeling for Stable RLHF: Detecting and Mitigating Reward Hacking](https://mlsanity.com/paper/2510.13694/) (2025)
- [Improved Bounds for Private and Robust Alignment](https://mlsanity.com/paper/2512.23816/) (2025)

## Abstract (arXiv)

Language model alignment methods such as reinforcement learning from human feedback (RLHF) have led to impressive advances in language model capabilities, but are limited by a widely observed phenomenon known as overoptimization, where the quality of the language model degrades over the course of the alignment process. As the model optimizes performance with respect to an offline reward model, it overfits to inaccuracies and drifts away from preferred responses covered by the data. To discourage such distribution shift, KL-regularization is widely employed in existing offline alignment methods, but overoptimization continues to harm performance. Lending theoretical insight into the source of these empirical observations, we first show that the KL-regularization is too weak to prevent overfitting, then raise the following question: is it possible to design an efficient algorithm that is provably robust to overoptimization? We address this question with a new algorithm for offline alignment, chi2-Preference Optimization (chiPO). chiPO is a one-line change to Direct Preference Optimization (DPO; Rafailov et al., 2023), which only involves modifying the logarithmic link function in the DPO objective. Despite this minimal change, chiPO implicitly implements the principle of pessimism in the face of uncertainty via regularization with the chi2-divergence -- which quantifies uncertainty more effectively than KL-regularization -- and provably alleviates overoptimization, achieving sample-complexity guarantees based on single-policy concentrability -- the gold standard in offline reinforcement learning. chiPO's simplicity and strong guarantees make it the first practical and general-purpose offline alignment algorithm that is provably robust to overoptimization.