用流匹配模型直接优化设计分布，高效逼近帕累托前沿。
ParetoTransport: Generative Optimization by Mass Transport Toward The Pareto Front
- 通过水波斯坦距离引导采样器迭代运输分布至帕累托前沿。
- 在标准离线多目标优化基准上达到顶尖性能，覆盖多种评估指标。
- 无需训练，可直接作用于预训练流匹配模型，适合快速部署。
离线多目标优化不仅需要将候选设计的目标向量移向帕累托前沿，还需有效分布于其上。生成方法因其学习可行设计分布的能力而成为自然选择，但现有方法仍沿用传统逐样本指导策略，未充分挖掘生成模型的分布建模潜力。我们提出ParetoTransport，一种针对预训练流匹配模型的无训练引导方法，可显式指定并精炼目标空间中的群体分布。该方法引导流匹配采样器通过水波斯坦匹配中间代理分布，迭代地将经验分布运送到帕累托前沿，直接控制分布位移与前沿上的质量分配。我们建立了收敛性结果，并在标准离线多目标优化基准上实现领先表现，扩展了近期评估范围，涵盖超体积、生成距离、反向生成距离及水波斯坦距离。
原文摘要 · Abstract (English)
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.
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