Many-Objective Multi-Solution Transport

Optimizing the performance of many objectives (instantiated by tasks or clients) jointly with a few Pareto stationary solutions (models) is critical in machine learning. However, previous multi-objective optimization methods often focus on a few objectives and cannot scale to many objectives that outnumber the solutions, leading to either subpar performance or ignored objectives. We introduce ''Many-objective multi-solution Transport (MosT)'', a framework that finds multiple diverse solutions in the Pareto front of many objectives. Our insight is to seek multiple solutions, each performing as a domain expert and focusing on a specific subset of objectives while collectively covering all of them. MosT formulates the problem as a bi-level optimization of weighted objectives for each solution, where the weights are defined by an optimal transport between objectives and solutions. Our algorithm ensures convergence to Pareto stationary solutions for complementary subsets of objectives. On a range of applications in federated learning, multi-task learning, and mixture-of-prompt learning for LLMs, MosT distinctly outperforms strong baselines, delivering high-quality, diverse solutions that profile the entire Pareto frontier, thus ensuring balanced trade-offs across many objectives.