Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond

Multi-objective optimization (MOO) in deep learning aims to simultaneously optimize multiple conflicting objectives, a challenge frequently encountered in areas like multi-task learning and multi-criteria learning. Recent advancements in gradient-based MOO methods have enabled the discovery of diverse types of solutions, ranging from a single balanced solution to finite or even infinite Pareto sets, tailored to user needs. These developments have broad applications across domains such as reinforcement learning, computer vision, recommendation systems, and large language models. This survey provides the first comprehensive review of gradient-based MOO in deep learning, covering algorithms, theories, and practical applications. By unifying various approaches and identifying critical challenges, it serves as a foundational resource for driving innovation in this evolving field. A comprehensive list of MOO algorithms in deep learning is available at \url{https://github.com/Baijiong-Lin/Awesome-Multi-Objective-Deep-Learning}.