Multi-Objective Multi-Solution Transport
Primary Area: optimization
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Keywords: Multi-Objective Optimization
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Abstract: In the realm of multi-objective optimization, we introduce ''Multi-objective multi-solution Transport (MosT)'', a novel solution for optimizing multiple objectives that employs multiple solutions. The essence lies in achieving diverse trade-offs among objectives, where each solution performs as a domain expert, focusing on specific objectives while collectively covering all of them. Traditional methods often struggle, especially when the number of objectives greatly outnumbers the number of solutions, leading to either subpar solutions or objectives that have been essentially ignored. MosT addresses this by formulating the problem as a bi-level optimization of weighted objectives, where the weights are defined by an optimal transport between the objectives and solutions. Our newly developed algorithm not only ensures theoretical convergence to various Pareto front solutions but is also adaptive to cases where objectives outnumber solutions. We further enhance its efficiency by introducing a solution-specialization curriculum. With proven applications in federated learning, fairness-accuracy trade-offs, and standard MOO benchmarks, MosT distinctly outperforms existing methods, delivering high-quality, diverse solutions that profile the entire Pareto frontier, thus ensuring balanced trade-offs across objectives.
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Submission Number: 8707
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