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

TL;DR

MGDA-Decoupled is a geometry-aware multi-objective optimisation algorithm designed for aligning large language models, promoting fairer trade-offs among conflicting objectives within the DPO framework.

Contribution

It introduces a novel geometry-based optimisation method that explicitly considers each objective's convergence dynamics, improving fairness and effectiveness in LLM alignment.

Findings

MGDA-Decoupled achieves the highest win rates against golden responses.

Geometry-aware methods outperform prior approaches on the UltraFeedback dataset.

The approach operates entirely within the lightweight DPO paradigm.

Abstract

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.