Multi-Objective Optimization for Modern Machine Learning: Foundations, Recent Advances, and Emerging Applications

Machine learning (ML) tasks are increasingly required to satisfy multiple, often competing, objectives simultaneously. Multi-objective optimization (MOO) provides a principled mathematical framework for modeling and solving such problems by systematically characterizing trade-offs among conflicting goals and identifying Pareto-optimal solutions. This tutorial introduces the foundations and recent advances of MOO for machine learning and artificial intelligence. We begin with fundamental concepts, such as Pareto optimality, Pareto fronts, scalarization techniques, preference-based optimization, and gradient-based approaches. We then present modern algorithmic developments that have significantly expanded the applicability of MOO in complex machine learning settings, including distributed MOO, multi-objective bilevel optimization for hierarchical decision-making, multi-objective reinforcement learning, and their use cases. The tutorial is designed for a broad NeurIPS audience, including graduate students, researchers, and practitioners working in ML, artificial intelligence (AI), and optimization-related fields. We will focus on state-of-the-art algorithmic and theoretical developments, while also emphasizing intuition and connections to ML applications.