# On the Role of Preference Variance in Preference Optimization

arXiv: https://arxiv.org/abs/2510.13022 · HTML: https://mlsanity.com/paper/2510.13022/

## Key facts

- Cited by 3 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 58 of its 71 references that are in the map.
- First posted on arXiv 14 Oct 2025.

## 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 58)

- [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)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback](https://mlsanity.com/paper/2305.14387/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [ORPO: Monolithic Preference Optimization without Reference Model](https://mlsanity.com/paper/2403.07691/) (2024)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [From Crowdsourced Data to High-Quality Benchmarks: Arena-Hard and BenchBuilder Pipeline](https://mlsanity.com/paper/2406.11939/) (2024)
- [Dataset Cartography: Mapping and Diagnosing Datasets with Training Dynamics](https://mlsanity.com/paper/2009.10795/) (2020)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [Skywork-Reward: Bag of Tricks for Reward Modeling in LLMs](https://mlsanity.com/paper/2410.18451/) (2024)
- [PEBBLE: Feedback-Efficient Interactive Reinforcement Learning via Relabeling Experience and Unsupervised Pre-training](https://mlsanity.com/paper/2106.05091/) (2021)
- [Preference Ranking Optimization for Human Alignment](https://mlsanity.com/paper/2306.17492/) (2023)
- [Large Language Model Alignment: A Survey](https://mlsanity.com/paper/2309.15025/) (2023)
- [Self-Play Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2405.00675/) (2024)
- [Superfiltering: Weak-to-Strong Data Filtering for Fast Instruction-Tuning](https://mlsanity.com/paper/2402.00530/) (2024)
- [DPO Meets PPO: Reinforced Token Optimization for RLHF](https://mlsanity.com/paper/2404.18922/) (2024)
- [MaxMin-RLHF: Alignment with Diverse Human Preferences](https://mlsanity.com/paper/2402.08925/) (2024)
- [Dueling RL: Reinforcement Learning with Trajectory Preferences](https://mlsanity.com/paper/2111.04850/) (2021)

## Built on by (most cited first, 3 of 3)

- [GenEnv: Difficulty-Aligned Co-Evolution Between LLM Agents and Environment Simulators](https://mlsanity.com/paper/2512.19682/) (2025)
- [What Does Preference Learning Recover from Pairwise Comparison Data?](https://mlsanity.com/paper/2602.10286/) (2026)
- [To Go Far, Go Together: Diverse Preferences Induce a Curriculum for Reward Optimization](https://mlsanity.com/paper/2608.18770/) (2026)

## Abstract (arXiv)

Direct Preference Optimization (DPO) has emerged as an important approach for learning from human preferences in aligning large language models (LLMs). However, collecting human preference data is costly and inefficient, motivating methods to reduce the required annotations. In this work, we investigate the impact of preference variance (PVar), which measures the variance in model preferences when comparing pairs of responses, on the effectiveness of DPO training. We provide a theoretical insight by establishing an upper bound on the DPO gradient norm for any given prompt, showing it is controlled by the PVar of that prompt. This implies that prompts with low PVar can only produce small gradient updates, making them less valuable for learning. We validate this finding by fine-tuning LLMs with preferences generated by a reward model, evaluating on two benchmarks (AlpacaEval 2.0 and Arena-Hard). Experimental results demonstrate that prompts with higher PVar outperform randomly selected prompts or those with lower PVar. We also show that our PVar-based selection method is robust, when using smaller reward models (1B, 3B) for selection. Notably, in a separate experiment using the original human annotations from the UltraFeedback dataset, we found that training on only the top 10% of prompts with the highest PVar yields better evaluation performance than training on the full dataset, highlighting the importance of preference variance in identifying informative examples for efficient LLM alignment.