Three-Way Trade-Off in Multi-Objective Learning: Optimization, Generalization and Conflict-Avoidance

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. Code is available at https://github.com/heshandevaka/Trade-Off-MOL.