  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.
