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This research introduces ParetoTransport, a training-free guidance method for flow-matching models that optimizes distributional displacement in offline multi-objective optimization. By leveraging Wasserstein matching to steer empirical distributions toward the Pareto front, the approach achieves state-of-the-art performance on standard benchmarks while addressing limitations in existing sample-wise strategies. The work advances generative methods by explicitly refining population-level distributions rather than relying on classical guidance techniques.
ParetoTransport: Generative Optimization by Mass Transport Toward The Pareto Front
arXiv:2609.07706v1 Announce Type: new Abstract: Offline multi-objective optimization requires not only moving the objective vectors of candidate designs toward the Pareto front, but also distributing them effectively along it. Generative methods have recently emerged as a natural approach because they learn a distribution over feasible designs while allowing generation to be steered toward promising designs. Existing methods, however, largely retain classical sample-wise guidance strategies, leaving the distribution-level modeling capability of generative methods underused. We propose ParetoTransport, a training-free guidance method for pre-trained flow-matching models that explicitly specifies and refines a population-level distribution in objective space. ParetoTransport guides a flow-matching sampler to iteratively transport the empirical offline distribution toward the Pareto front, with Wasserstein matching to intermediate proxy distributions. This directly controls distributional displacement and mass allocation along the front. We establish a convergence result and demonstrate state-of-the-art performance on standard offline MOO benchmarks, extending recent evaluations beyond hypervolume to generational distance, inverted generational distance, and Wasserstein distance.
Abstract:Offline multi-objective optimization requires not only moving the objective vectors of candidate designs toward the Pareto front, but also distributing them effectively along it. Generative methods have recently emerged as a natural approach because they learn a distribution over feasible designs while allowing generation to be steered toward promising designs. Existing methods, however, largely retain classical sample-wise guidance strategies, leaving the distribution-level modeling capability of generative methods underused. We propose ParetoTransport, a training-free guidance method for pre-trained flow-matching models that explicitly specifies and refines a population-level distribution in objective space. ParetoTransport guides a flow-matching sampler to iteratively transport the empirical offline distribution toward the Pareto front, with Wasserstein matching to intermediate proxy distributions. This directly controls distributional displacement and mass allocation along the front. We establish a convergence result and demonstrate state-of-the-art performance on standard offline MOO benchmarks, extending recent evaluations beyond hypervolume to generational distance, inverted generational distance, and Wasserstein distance.
Machine Learning (cs.LG)
arXiv:2609.07706 [cs.LG]
(or arXiv:2609.07706v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.07706 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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