Multi-objective learning (MOL) often arises in emerging machine learning problems when multiple learning criteria or tasks need to be addressed. Recent works have developed various _dynamic weighting_ algorithms for MOL, including MGDA and its variants, whose 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 alternatives. To bridge this gap between theory and practice, we focus on a new variant of stochastic MGDA - the Multi-objective gradient with Double sampling (MoDo) algorithm and study its generalization performance and the interplay with optimization through the lens of algorithm stability. We find that the rationale behind MGDA -- updating along conflict-avoidant direction - may \emph{impede} dynamic weighting algorithms from achieving the optimal ${\cal O}(1/\sqrt{n})$ population risk, where $n$ is the number of training samples. We further highlight the variability of dynamic weights and their impact on the three-way trade-off among optimization, generalization, and conflict avoidance that is unique in MOL.

Multi-objective learning (MOL) often arises in emerging machine learning problems when multiple learning criteria or tasks need to be addressed. Recent works have developed various _dynamic weighting_ algorithms for MOL, including MGDA and its variants, whose 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 alternatives. To bridge this gap between theory and practice, we focus on a new variant of stochastic MGDA - the Multi-objective gradient with Double sampling (MoDo) algorithm and study its generalization performance and the interplay with optimization through the lens of algorithm stability. We find that the rationale behind MGDA -- updating along conflict-avoidant direction - may \emph{impede} dynamic weighting algorithms from achieving the optimal {\cal O}(1/\sqrt{n}) population risk, where n is the number of training samples.

Multi-objective learning (MOL) problems often arise in emerging machine learning problems when there are multiple learning criteria, data modalities, or learning tasks. Different from single-objective learning, one of the critical challenges in MOL is the potential conflict among different objectives during the iterative optimization process. 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 impact of the variability of dynamic weights on the three-way trade-off among optimization, generalization, and conflict avoidance that is unique in MOL. We showcase the generality of our theoretical framework by analyzing other existing stochastic MOL algorithms under the framework. Experiments on various multi-task learning benchmarks are performed to demonstrate the practical applicability. Code is available at https://github.com/heshandevaka/Trade-Off-MOL.