# PEO: Improving Bi-Factorial Preference Alignment with Post-Training Policy Extrapolation

arXiv: https://arxiv.org/abs/2503.01233 · HTML: https://mlsanity.com/paper/2503.01233/

## Key facts

- Cited by 1 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 33 of its 52 references that are in the map.
- First posted on arXiv 3 Mar 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 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [BeaverTails: Towards Improved Safety Alignment of LLM via a Human-Preference Dataset](https://mlsanity.com/paper/2307.04657/) (2023)
- [Safe RLHF: Safe Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2310.12773/) (2023)
- [Bias and Fairness in Large Language Models: A Survey](https://mlsanity.com/paper/2309.00770/) (2023)
- [ORPO: Monolithic Preference Optimization without Reference Model](https://mlsanity.com/paper/2403.07691/) (2024)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervision](https://mlsanity.com/paper/2312.09390/) (2023)
- [Interpretable Preferences via Multi-Objective Reward Modeling and Mixture-of-Experts](https://mlsanity.com/paper/2406.12845/) (2024)
- [Personalized Soups: Personalized Large Language Model Alignment via Post-hoc Parameter Merging](https://mlsanity.com/paper/2310.11564/) (2023)
- [A Practical Guide to Multi-Objective Reinforcement Learning and Planning](https://mlsanity.com/paper/2103.09568/) (2021)
- [Smaug: Fixing Failure Modes of Preference Optimisation with DPO-Positive](https://mlsanity.com/paper/2402.13228/) (2024)
- [Reward Model Ensembles Help Mitigate Overoptimization](https://mlsanity.com/paper/2310.02743/) (2023)
- [Secrets of RLHF in Large Language Models Part I: PPO](https://mlsanity.com/paper/2307.04964/) (2023)
- [Helping or Herding? Reward Model Ensembles Mitigate but do not Eliminate Reward Hacking](https://mlsanity.com/paper/2312.09244/) (2023)
- [Rewards-in-Context: Multi-objective Alignment of Foundation Models with Dynamic Preference Adjustment](https://mlsanity.com/paper/2402.10207/) (2024)
- [Arithmetic Control of LLMs for Diverse User Preferences: Directional Preference Alignment with Multi-Objective Rewards](https://mlsanity.com/paper/2402.18571/) (2024)
- [Provably Robust DPO: Aligning Language Models with Noisy Feedback](https://mlsanity.com/paper/2403.00409/) (2024)
- [Beyond One-Preference-Fits-All Alignment: Multi-Objective Direct Preference Optimization](https://mlsanity.com/paper/2310.03708/) (2023)
- [Deep Reinforcement Learning from Policy-Dependent Human Feedback](https://mlsanity.com/paper/1902.04257/) (2019)
- [Chat Vector: A Simple Approach to Equip LLMs with Instruction Following and Model Alignment in New Languages](https://mlsanity.com/paper/2310.04799/) (2023)
- [The N+ Implementation Details of RLHF with PPO: A Case Study on TL;DR Summarization](https://mlsanity.com/paper/2403.17031/) (2024)

## Built on by (most cited first, 1 of 1)

- [Steerable Adversarial Scenario Generation through Test-Time Preference Alignment](https://mlsanity.com/paper/2509.20102/) (2025)

## Abstract (arXiv)

The alignment of large language models with human values presents a critical challenge, particularly when balancing conflicting objectives like helpfulness and harmlessness. Existing approaches, such as Reinforcement Learning from Human Feedback (RLHF) and Direct Preference Optimization (DPO), face notable limitations: RLHF suffers from instability and inefficiency in multi-objective optimization, while DPO lacks mechanisms for dynamic trade-offs. To address these challenges, we propose Post-Training Extrapolation Optimization (PEO), a novel and efficient framework for bi-factorial alignment. PEO generates a family of Pareto-optimal policies in a single training pass by leveraging a three-phase pipeline: (1) aspect-specific learning, (2) generalist initialization via interpolation, and (3) post-training optimization via extrapolation. PEO enables dynamic adaptation to diverse user preferences at inference time without retraining. Our comprehensive experiments across multiple LLMs demonstrate that PEO achieves superior Pareto fronts compared to baselines, offering improved flexibility and computational efficiency. Theoretical analyses further highlight PEO's capacity to overcome optimization bottlenecks, paving the way for scalable, personalized alignment.