# A Unified Framework for Gradient Aggregation in Multi-Objective Optimization

arXiv: https://arxiv.org/abs/2605.30452 · HTML: https://mlsanity.com/paper/2605.30452/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 17 of 17)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [Multi-Task Learning as a Bargaining Game](https://mlsanity.com/paper/2202.01017/) (2022)
- [Reasonable Effectiveness of Random Weighting: A Litmus Test for Multi-Task Learning](https://mlsanity.com/paper/2111.10603/) (2021)
- [The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learning](https://mlsanity.com/paper/1907.04472/) (2019)
- [ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks](https://mlsanity.com/paper/2408.11104/) (2024)
- [Three-Way Trade-Off in Multi-Objective Learning: Optimization, Generalization and Conflict-Avoidance](https://mlsanity.com/paper/2305.20057/) (2023)
- [Fair Resource Allocation in Multi-Task Learning](https://mlsanity.com/paper/2402.15638/) (2024)
- [Direction-oriented Multi-objective Learning: Simple and Provable Stochastic Algorithms](https://mlsanity.com/paper/2305.18409/) (2023)
- [Dual Cone Gradient Descent for Training Physics-Informed Neural Networks](https://mlsanity.com/paper/2409.18426/) (2024)
- [Jacobian Descent for Multi-Objective Optimization](https://mlsanity.com/paper/2406.16232/) (2024)
- [LibMOON: A Gradient-based MultiObjective OptimizatioN Library in PyTorch](https://mlsanity.com/paper/2409.02969/) (2024)
- [MGDA Converges under Generalized Smoothness, Provably](https://mlsanity.com/paper/2405.19440/) (2024)
- [An accelerated proximal gradient method for multiobjective optimization](https://mlsanity.com/paper/2202.10994/) (2022)

## Abstract (arXiv)

Many machine learning problems involve multiple inherent trade-offs that are best addressed by gradient-based multi-objective optimization (MOO) algorithms. Existing methods are often proposed with various motivations, analyzed case by case, and differ algorithmically in how the component gradients are aggregated at each step. In this work, we develop a unifying framework for gradient aggregation in MOO, establishing (optimal) rates of convergence to Pareto stationarity, the standard measure of performance in MOO. Central to our analysis is a sufficient alignment condition, from which we derive a theorem showing that non-conflicting directions, when chosen within the convex hull of gradients, form a fundamental sufficient condition for convergence. We further show that feasibility can be ensured through projection onto the dual cone, broadening the scope of methods that admit convergence guarantees. In parallel, we present a primal optimization perspective of gradient aggregation that encompasses established algorithms, clarifies their theoretical relationships, and enables the design of new variants. As an illustration, we introduce capped MGDA, derived from a CVaR-based formulation, and demonstrate its robustness in adversarial federated learning. Finally, we validate our theory through experiments on synthetic problems and practical benchmarks.