# Regularity-Aware Stochastic MGDA with Adaptive Conflict-Avoidant Update Direction Control

arXiv: https://arxiv.org/abs/2607.15412 · HTML: https://mlsanity.com/paper/2607.15412/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 16 Jul 2026.

## Builds on (most cited first, 10 of 10)

- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [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)
- [The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learning](https://mlsanity.com/paper/1907.04472/) (2019)
- [Multi-Objective Meta Learning](https://mlsanity.com/paper/2102.07121/) (2021)
- [Three-Way Trade-Off in Multi-Objective Learning: Optimization, Generalization and Conflict-Avoidance](https://mlsanity.com/paper/2305.20057/) (2023)
- [Direction-oriented Multi-objective Learning: Simple and Provable Stochastic Algorithms](https://mlsanity.com/paper/2305.18409/) (2023)
- [Learning with Limited Samples -- Meta-Learning and Applications to Communication Systems](https://mlsanity.com/paper/2210.02515/) (2022)
- [FERERO: A Flexible Framework for Preference-Guided Multi-Objective Learning](https://mlsanity.com/paper/2412.01773/) (2024)

## Abstract (arXiv)

Multi-objective learning (MOL) aims to optimize multiple objectives simultaneously. The multi-gradient descent algorithm (MGDA) is a workhorse that iteratively updates along a common descent or conflict-avoidant (CA) direction across objectives. In stochastic settings, however, the vanilla stochastic MGDA method, SMG, lacks a fast convergence rate because mini-batch sampling introduces noise in the gradients. This causes bias in the update direction, which is controlled by the CA direction continuity. In this paper, we show that the CA direction is 1/2-Holder continuous with respect to the Jacobian matrix, and the exponent 1/2 cannot be improved in the worst case. This leads to a suboptimal convergence rate for vanilla stochastic MGDA in prior works. Nevertheless, under additional regularity conditions, we show this can be improved to Lipschitz continuity. Based on this insight, we propose a stochastic multi-objective regularity-aware (MoRe) method that exploits the Lipschitz continuity of the CA direction when the subproblem is regular, and switches to a fixed scalarization weight otherwise. Intuitively, the proposed algorithm employs CA direction update when the gradient conflict is large, and linear scalarization update otherwise. Theoretically, our method improves the convergence rate of SMG in the nonconvex setting from widetildemathcal O(T-1/4) to widetildemathcal O(T-1/2), where widetildemathcal O(·) hides logarithmic factors. Meanwhile, we also establish the per-iterate conflict-avoidance guarantees. Empirically, experiments demonstrate its effectiveness in multi-task performance and verify convergence behavior consistent with the established theoretical rate.