Gradient-based Methods for Multi-Objective Optimization with Applications in Machine Learning

Abstract

Many machine learning problems involve trade-offs among multiple objectives, such as accuracy, fairness, or the interests of different tasks or users, making multi-objective optimization (MOO) a natural framework for their study. Such trade-offs arise in a range of modern machine learning settings, including but not limited to multi-task learning, federated learning, algorithmic fairness, and reinforcement learning. While MOO has long been studied in the optimization literature, often through classical approaches such as evolutionary algorithms, contemporary machine learning problems are typically high-dimensional and call for scalable gradient-based methods. This thesis studies gradient-based MOO from three complementary perspectives: its application to federated learning as an important machine learning setting, the refinement of its solution concepts under variable sparsity, and the development of a unifying theory for gradient aggregation methods.