# MGDA-Decoupled: Geometry-Aware Multi-Objective Optimisation for DPO-based LLM Alignment

arXiv: https://arxiv.org/abs/2604.20685 · HTML: https://mlsanity.com/paper/2604.20685/

## 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 32 of its 44 references that are in the map.
- First posted on arXiv 22 Apr 2026.

## 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 32)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [A General Language Assistant as a Laboratory for Alignment](https://mlsanity.com/paper/2112.00861/) (2021)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [Fine-Grained Human Feedback Gives Better Rewards for Language Model Training](https://mlsanity.com/paper/2306.01693/) (2023)
- [Rewarded soups: towards Pareto-optimal alignment by interpolating weights fine-tuned on diverse rewards](https://mlsanity.com/paper/2306.04488/) (2023)
- [Mitigating the Alignment Tax of RLHF](https://mlsanity.com/paper/2309.06256/) (2023)
- [Rewards-in-Context: Multi-objective Alignment of Foundation Models with Dynamic Preference Adjustment](https://mlsanity.com/paper/2402.10207/) (2024)
- [Qwen2.5-1M Technical Report](https://mlsanity.com/paper/2501.15383/) (2025)
- [Arithmetic Control of LLMs for Diverse User Preferences: Directional Preference Alignment with Multi-Objective Rewards](https://mlsanity.com/paper/2402.18571/) (2024)
- [Beyond One-Preference-Fits-All Alignment: Multi-Objective Direct Preference Optimization](https://mlsanity.com/paper/2310.03708/) (2023)
- [MaxMin-RLHF: Alignment with Diverse Human Preferences](https://mlsanity.com/paper/2402.08925/) (2024)
- [Controllable Preference Optimization: Toward Controllable Multi-Objective Alignment](https://mlsanity.com/paper/2402.19085/) (2024)
- [Value Kaleidoscope: Engaging AI with Pluralistic Human Values, Rights, and Duties](https://mlsanity.com/paper/2309.00779/) (2023)
- [Panacea: Pareto Alignment via Preference Adaptation for LLMs](https://mlsanity.com/paper/2402.02030/) (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)
- [Gradient-Adaptive Policy Optimization: Towards Multi-Objective Alignment of Large Language Models](https://mlsanity.com/paper/2507.01915/) (2025)
- [Robust Multi-Objective Preference Alignment with Online DPO](https://mlsanity.com/paper/2503.00295/) (2025)
- [RainbowPO: A Unified Framework for Combining Improvements in Preference Optimization](https://mlsanity.com/paper/2410.04203/) (2024)
- [Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond](https://mlsanity.com/paper/2501.10945/) (2025)

## Abstract (arXiv)

Aligning large language models (LLMs) to desirable human values requires balancing multiple, potentially conflicting objectives such as helpfulness, truthfulness, and harmlessness, which presents a multi-objective optimisation challenge. Most alignment pipelines rely on a fixed scalarisation of these objectives, which can introduce procedural unfairness by systematically under-weighting harder-to-optimise or minority objectives. To promote more equitable trade-offs, we introduce MGDA-Decoupled, a geometry-based multi-objective optimisation algorithm that finds a shared descent direction while explicitly accounting for each objective's convergence dynamics. In contrast to prior methods that depend on reinforcement learning (e.g., GAPO) or explicit reward models (e.g., MODPO), our approach operates entirely within the lightweight Direct Preference Optimisation (DPO) paradigm. Experiments on the UltraFeedback dataset show that geometry-aware methods -- and MGDA-Decoupled in particular -- achieve the highest win rates against golden responses, both overall and per objective.