# Provably Convergent Primal-Dual DPO for Constrained LLM Alignment

arXiv: https://arxiv.org/abs/2510.05703 · HTML: https://mlsanity.com/paper/2510.05703/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 27 of its 50 references that are in the map.
- First posted on arXiv 7 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, 27 of 27)

- [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)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Jailbroken: How Does LLM Safety Training Fail?](https://mlsanity.com/paper/2307.02483/) (2023)
- [RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Models](https://mlsanity.com/paper/2009.11462/) (2020)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [Safe RLHF: Safe Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2310.12773/) (2023)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Is DPO Superior to PPO for LLM Alignment? A Comprehensive Study](https://mlsanity.com/paper/2404.10719/) (2024)
- [Principled Reinforcement Learning with Human Feedback from Pairwise or K-wise Comparisons](https://mlsanity.com/paper/2301.11270/) (2023)
- [Exploration-Exploitation in Constrained MDPs](https://mlsanity.com/paper/2003.02189/) (2020)
- [Aligner: Efficient Alignment by Learning to Correct](https://mlsanity.com/paper/2402.02416/) (2024)
- [PC-PG: Policy Cover Directed Exploration for Provable Policy Gradient Learning](https://mlsanity.com/paper/2007.08459/) (2020)
- [Enhancing LLM Safety via Constrained Direct Preference Optimization](https://mlsanity.com/paper/2403.02475/) (2024)
- [MetaAligner: Towards Generalizable Multi-Objective Alignment of Language Models](https://mlsanity.com/paper/2403.17141/) (2024)
- [SafeDPO: A Simple Approach to Direct Preference Optimization with Enhanced Safety](https://mlsanity.com/paper/2505.20065/) (2025)
- [Stepwise Alignment for Constrained Language Model Policy Optimization](https://mlsanity.com/paper/2404.11049/) (2024)
- [One-Shot Safety Alignment for Large Language Models via Optimal Dualization](https://mlsanity.com/paper/2405.19544/) (2024)
- [Alignment of large language models with constrained learning](https://mlsanity.com/paper/2505.19387/) (2025)
- [MidPO: Dual Preference Optimization for Safety and Helpfulness in Large Language Models via a Mixture of Experts Framework](https://mlsanity.com/paper/2506.02460/) (2025)

## Abstract (arXiv)

The widespread application of large language models (LLMs) raises increasing demands on ensuring safety or imposing constraints, such as reducing harmful content and adhering to predefined rules. While there have been several works studying LLM safety alignment, these works either need to train three models and incur high memory costs, or require prior knowledge on the optimal solution. Witnessing this fact, we investigate the constrained alignment problem for LLMs, i.e., maximizing the reward of outputs while restricting the cost to stay below a threshold. We propose a novel primal-dual direct preference optimization (DPO) approach, which first trains a model using standard DPO on reward preference data to provide reward information, and then adopts a rearranged Lagrangian DPO objective utilizing the provided reward information to fine-tune LLMs. Our approach only needs to train two models rather than three, which significantly saves memory costs, and does not require extra prior knowledge. Moreover, we establish rigorous suboptimality and constraint violation guarantees. We also extend our approach to enable online exploration and drop the data coverage dependence in the results. Experiments on the PKU-SafeRLHF and TruthfulQA datasets demonstrate the state-of-the-art performance of our approach.