Multi-objective learning (MOL) problems often arise in emerging machine learning problems when there are multiple learning criteria or multiple learning tasks. Recent works have developed various dynamic weighting algorithms for MOL such as MGDA and its variants, where the central idea is to find an update direction that avoids conflicts among objectives. Albeit its appealing intuition, empirical studies show that dynamic weighting methods may not always outperform static ones. To understand this theory-practical gap, we focus on a new stochastic variant of MGDA - the Multi-objective gradient with Double sampling (MoDo) algorithm, and study the generalization performance of the dynamic weighting-based MoDo and its interplay with optimization through the lens of algorithm stability. Perhaps surprisingly, we find that the key rationale behind MGDA -- updating along conflict-avoidant direction - may hinder dynamic weighting algorithms from achieving the optimal ${\cal O}(1/\sqrt{n})$ population risk, where $n$ is the number of training samples. We further demonstrate the variability of dynamic weights on the three-way trade-off among optimization, generalization, and conflict avoidance that is unique in MOL.

翻译：多目标学习问题频繁出现在新兴机器学习任务中，当存在多个学习准则或多个学习任务时尤为突出。近期研究开发了多种面向多目标学习的动态权重算法，如MGDA及其变体，其核心思想是寻找能避免目标间冲突的更新方向。尽管这一直觉颇具吸引力，但实证研究表明动态权重方法未必始终优于静态方法。为理解这一理论与实践的差距，我们聚焦于MGDA的一种新随机变体——双重采样多目标梯度算法，通过算法稳定性视角研究基于动态权重的MoDo的泛化性能及其与优化的相互作用。出人意料的是，我们发现MGDA的关键原理（即沿避免冲突方向更新）可能阻碍动态权重算法实现最优的${\cal O}(1/\sqrt{n})$群体风险（其中$n$为训练样本数）。我们进一步揭示了动态权重在多目标学习独有的优化、泛化与冲突规避三重权衡中的可变性。