# Geometric-Averaged Preference Optimization for Soft Preference Labels

arXiv: https://arxiv.org/abs/2409.06691 · HTML: https://mlsanity.com/paper/2409.06691/

## Key facts

- Cited by 18 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 56 of its 66 references that are in the map.
- First posted on arXiv 10 Sep 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 56)

- [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)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [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)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Large Language Models are not Fair Evaluators](https://mlsanity.com/paper/2305.17926/) (2023)
- [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)
- [BeaverTails: Towards Improved Safety Alignment of LLM via a Human-Preference Dataset](https://mlsanity.com/paper/2307.04657/) (2023)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [Can Large Language Models Be an Alternative to Human Evaluations?](https://mlsanity.com/paper/2305.01937/) (2023)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [Symmetric Cross Entropy for Robust Learning with Noisy Labels](https://mlsanity.com/paper/1908.06112/) (2019)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [SLiC-HF: Sequence Likelihood Calibration with Human Feedback](https://mlsanity.com/paper/2305.10425/) (2023)
- [Statistical Rejection Sampling Improves Preference Optimization](https://mlsanity.com/paper/2309.06657/) (2023)
- [Preference Ranking Optimization for Human Alignment](https://mlsanity.com/paper/2306.17492/) (2023)
- [Critic Regularized Regression](https://mlsanity.com/paper/2006.15134/) (2020)
- [Large Language Models Sensitivity to The Order of Options in Multiple-Choice Questions](https://mlsanity.com/paper/2308.11483/) (2023)
- [Is DPO Superior to PPO for LLM Alignment? A Comprehensive Study](https://mlsanity.com/paper/2404.10719/) (2024)
- [Direct Language Model Alignment from Online AI Feedback](https://mlsanity.com/paper/2402.04792/) (2024)

## Built on by (most cited first, 18 of 18)

- [Plan-and-Act: Improving Planning of Agents for Long-Horizon Tasks](https://mlsanity.com/paper/2503.09572/) (2025)
- [Improving Dynamic Object Interactions in Text-to-Video Generation with AI Feedback](https://mlsanity.com/paper/2412.02617/) (2024)
- [Inference-Time Text-to-Video Alignment with Diffusion Latent Beam Search](https://mlsanity.com/paper/2501.19252/) (2025)
- [A Survey of Direct Preference Optimization](https://mlsanity.com/paper/2503.11701/) (2025)
- [Beyond Bradley-Terry Models: A General Preference Model for Language Model Alignment](https://mlsanity.com/paper/2410.02197/) (2024)
- [Genius: A Generalizable and Purely Unsupervised Self-Training Framework For Advanced Reasoning](https://mlsanity.com/paper/2504.08672/) (2025)
- [Pairwise Calibrated Rewards for Pluralistic Alignment](https://mlsanity.com/paper/2506.06298/) (2025)
- [Sail into the Headwind: Alignment via Robust Rewards and Dynamic Labels against Reward Hacking](https://mlsanity.com/paper/2412.09544/) (2024)
- [Smoothed Preference Optimization via ReNoise Inversion for Aligning Diffusion Models with Varied Human Preferences](https://mlsanity.com/paper/2506.02698/) (2025)
- [VideoSAVi: Self-Aligned Video Language Models without Human Supervision](https://mlsanity.com/paper/2412.00624/) (2024)
- [DCRM: A Heuristic to Measure Response Pair Quality in Preference Optimization](https://mlsanity.com/paper/2506.14157/) (2025)
- [Deltaynamics: Language-Based Representation for Inferring Rigid-Body Dynamics From Videos](https://mlsanity.com/paper/2605.20576/) (2026)
- [Gaze patterns predict preference and confidence in pairwise AI image evaluation](https://mlsanity.com/paper/2603.24849/) (2026)
- [References Indeed Matter? Reference-Free Preference Optimization for Conversational Query Reformulation](https://mlsanity.com/paper/2505.06552/) (2025)
- [Tracing How Annotators Think: Augmenting Preference Judgments with Reading Processes](https://mlsanity.com/paper/2511.21912/) (2025)
- [Disentangling Optimization Scale from Preference Scale in DPO](https://mlsanity.com/paper/2608.27032/) (2026)
- [Towards Bridging the Gap Between Offline and Iterative Alignment via Preference Distillation](https://mlsanity.com/paper/2609.06893/) (2026)
- [Robust Nash Alignment under Preference Uncertainty](https://mlsanity.com/paper/2610.00715/) (2026)

## Abstract (arXiv)

Many algorithms for aligning LLMs with human preferences assume that human preferences are binary and deterministic. However, human preferences can vary across individuals, and therefore should be represented distributionally. In this work, we introduce the distributional soft preference labels and improve Direct Preference Optimization (DPO) with a weighted geometric average of the LLM output likelihood in the loss function. This approach adjusts the scale of learning loss based on the soft labels such that the loss would approach zero when the responses are closer to equally preferred. This simple modification can be easily applied to any DPO-based methods and mitigate over-optimization and objective mismatch, which prior works suffer from. Our experiments simulate the soft preference labels with AI feedback from LLMs and demonstrate that geometric averaging consistently improves performance on standard benchmarks for alignment research. In particular, we observe more preferable responses than binary labels and significant improvements where modestly-confident labels are in the majority.