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

2025-01-19

AI Summary

Deep learning multi-objective optimization (MOO) faces fundamental challenges in simultaneously achieving convergence, fairness, and scalability under objective conflicts. To address this, we establish the first comprehensive “theory–algorithm–application” framework for gradient-driven MOO. We propose a customizable solution-set taxonomy that unifies modeling of single-point equilibrium solutions, finite Pareto sets, and infinite Pareto fronts. Methodologically, our framework integrates gradient projection, scalarization, hypergradient optimization, implicit differentiation, and Pareto-front tracking—spanning algorithms from single-step updates to dynamic weight evolution. We release an open-source, comprehensive MOO algorithm landscape on GitHub, already deployed across reinforcement learning, computer vision, recommendation systems, and large language models. This work provides a reproducible, scalable, and industrially applicable methodological foundation for multi-objective AI.

Technology Category

• Machine Learning: Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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}.

Problem

• Multi-Objective Optimization
• Deep Learning
• Conflicting Goals

Innovation

• Gradient-based Multi-objective Learning
• Comprehensive Review
• Theoretical Framework