# On the Algorithmic Bias of Aligning Large Language Models with RLHF: Preference Collapse and Matching Regularization

arXiv: https://arxiv.org/abs/2405.16455 · HTML: https://mlsanity.com/paper/2405.16455/

## Key facts

- Cited by 72 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 45 of its 74 references that are in the map.
- First posted on arXiv 26 May 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 45)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Whose Opinions Do Language Models Reflect?](https://mlsanity.com/paper/2303.17548/) (2023)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (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)
- [Annotators with Attitudes: How Annotator Beliefs And Identities Bias Toxic Language Detection](https://mlsanity.com/paper/2111.07997/) (2021)
- [A Survey of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2312.14925/) (2023)
- [Is DPO Superior to PPO for LLM Alignment? A Comprehensive Study](https://mlsanity.com/paper/2404.10719/) (2024)
- [From r to Q^*: Your Language Model is Secretly a Q-Function](https://mlsanity.com/paper/2404.12358/) (2024)
- [Nash Learning from Human Feedback](https://mlsanity.com/paper/2312.00886/) (2023)
- [Disentangling Length from Quality in Direct Preference Optimization](https://mlsanity.com/paper/2403.19159/) (2024)
- [Preference Fine-Tuning of LLMs Should Leverage Suboptimal, On-Policy Data](https://mlsanity.com/paper/2404.14367/) (2024)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)

## Built on by (most cited first, 30 of 72)

- [The Landscape of Agentic Reinforcement Learning for LLMs: A Survey](https://mlsanity.com/paper/2509.02547/) (2025)
- [Preserving Diversity in Supervised Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2408.16673/) (2024)
- [Towards Implicit Bias Detection and Mitigation in Multi-Agent LLM Interactions](https://mlsanity.com/paper/2410.02584/) (2024)
- [The Homogenizing Effect of Large Language Models on Human Expression and Thought](https://mlsanity.com/paper/2508.01491/) (2025)
- [Exploration vs Exploitation: Rethinking RLVR through Clipping, Entropy, and Spurious Reward](https://mlsanity.com/paper/2512.16912/) (2025)
- [Restoring Calibration for Aligned Large Language Models: A Calibration-Aware Fine-Tuning Approach](https://mlsanity.com/paper/2505.01997/) (2025)
- [Diverse Preference Learning for Capabilities and Alignment](https://mlsanity.com/paper/2511.08594/) (2025)
- [CS4: Measuring the Creativity of Large Language Models Automatically by Controlling the Number of Story-Writing Constraints](https://mlsanity.com/paper/2410.04197/) (2024)
- [Demystifying Group Relative Policy Optimization: Its Policy Gradient is a U-Statistic](https://mlsanity.com/paper/2603.01162/) (2026)
- [Predicting vs. Acting: A Trade-off Between World Modeling & Agent Modeling](https://mlsanity.com/paper/2407.02446/) (2024)
- [Dual Active Learning for Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2410.02504/) (2024)
- [Stepwise Guided Policy Optimization: Coloring your Incorrect Reasoning in GRPO](https://mlsanity.com/paper/2505.11595/) (2025)
- [Alignment and Safety in Large Language Models: Safety Mechanisms, Training Paradigms, and Emerging Challenges](https://mlsanity.com/paper/2507.19672/) (2025)
- [Fine-Tuning Attention Modules Only: Enhancing Weight Disentanglement in Task Arithmetic](https://mlsanity.com/paper/2407.07089/) (2024)
- [Pairwise Calibrated Rewards for Pluralistic Alignment](https://mlsanity.com/paper/2506.06298/) (2025)
- [Doubly Robust Alignment for Large Language Models](https://mlsanity.com/paper/2506.01183/) (2025)
- [Where does output diversity collapse in post-training?](https://mlsanity.com/paper/2604.16027/) (2026)
- [Fundamental Limits of Game-Theoretic LLM Alignment: Smith Consistency and Preference Matching](https://mlsanity.com/paper/2505.20627/) (2025)
- [Silenced Biases: The Dark Side LLMs Learned to Refuse](https://mlsanity.com/paper/2511.03369/) (2025)
- [Stackelberg Learning from Human Feedback: Preference Optimization as a Sequential Game](https://mlsanity.com/paper/2512.16626/) (2025)
- [Understanding Diversity Collapse in RLVR via the Lens of Overtraining](https://mlsanity.com/paper/2606.15455/) (2026)
- [SPARTA ALIGNMENT: Collectively Aligning Multiple Language Models through Combat](https://mlsanity.com/paper/2506.04721/) (2025)
- [Contextual Online Uncertainty-Aware Preference Learning for Human Feedback](https://mlsanity.com/paper/2504.19342/) (2025)
- [An Empirical Study of Group Conformity in Multi-Agent Systems](https://mlsanity.com/paper/2506.01332/) (2025)
- [Theoretical Tensions in RLHF: Reconciling Empirical Success with Inconsistencies in Social Choice Theory](https://mlsanity.com/paper/2506.12350/) (2025)
- [LLM Safety Alignment is Divergence Estimation in Disguise](https://mlsanity.com/paper/2502.00657/) (2025)
- [Do Large Language Models (Really) Need Statistical Foundations?](https://mlsanity.com/paper/2505.19145/) (2025)
- [Long-Tail Knowledge in Large Language Models: Taxonomy, Mechanisms, Interventions and Implications](https://mlsanity.com/paper/2602.16201/) (2026)
- [Beyond Marginal Distributions: A Framework to Evaluate the Representativeness of Demographic-Aligned LLMs](https://mlsanity.com/paper/2601.15755/) (2026)
- [CATTO: Balancing Preferences and Confidence in Language Models](https://mlsanity.com/paper/2601.23096/) (2026)

## Abstract (arXiv)

Accurately aligning large language models (LLMs) with human preferences is crucial for informing fair, economically sound, and statistically efficient decision-making processes. However, we argue that the predominant approach for aligning LLMs with human preferences through a reward model -- reinforcement learning from human feedback (RLHF) -- suffers from an inherent algorithmic bias due to its Kullback--Leibler-based regularization in optimization. In extreme cases, this bias could lead to a phenomenon we term preference collapse, where minority preferences are virtually disregarded. To mitigate this algorithmic bias, we introduce preference matching (PM) RLHF, a novel approach that provably aligns LLMs with the preference distribution of the reward model under the Bradley--Terry--Luce/Plackett--Luce model. Central to our approach is a PM regularizer that takes the form of the negative logarithm of the LLM's policy probability distribution over responses, which helps the LLM balance response diversification and reward maximization. Notably, we obtain this regularizer by solving an ordinary differential equation that is necessary for the PM property. For practical implementation, we introduce a conditional variant of PM RLHF that is tailored to natural language generation. Finally, we empirically validate the effectiveness of conditional PM RLHF through experiments on the OPT and Llama-family models, demonstrating a 29% to 41% improvement in alignment with human preferences, as measured by a certain metric, compared to standard RLHF.