发表机构
Halıcıoğlu Data Science Institute, UC San Diego; Department of Computer Science & Engineering, UC San Diego（加州大学圣迭戈分校哈勒奇奥卢数据科学研究所; 加州大学圣迭戈分校计算机科学与工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出基于噪声空间几何的离线多目标优化方法，通过递归特征机估计敏感方向并位移初始噪声，以低采样成本引导扩散模型生成帕累托前沿解，在47个任务上取得最佳平均超体积排名。
AI 中文摘要
离线多目标优化（MOO）旨在仅使用固定数据集、在不查询目标函数的情况下，寻找具有更优目标权衡的解。基于此类数据训练的扩散模型已成为一种有前景的方法，但其样本本质上并不优于数据，必须将其引导至帕累托前沿。现有方法对每个采样步骤进行引导或条件化。我们转而作用于初始噪声，保持采样过程不变。在Off-MOO-Bench基准上，我们观察到目标函数作为噪声的函数，仅对少数方向敏感。我们通过递归特征机（Recursive Feature Machine）仅利用函数值，为每个任务估计一次这些方向，一个小型缓存即可服务所有权衡，因此每个候选解只需一次噪声位移和一次常微分方程（ODE）求解。我们证明该位移在期望上提高了学习的标量化目标，并且扫描权衡可恢复流可达到的前沿，直至代理误差和转向误差。结合额外引导（为此我们引入了新颖的数据自适应和帕累托感知算子），我们的方法在47个任务上取得了生成方法中最优的平均超体积排名，且采样成本相当或更低。仅转向方法即以一小部分采样成本超越了先前最优的生成方法。
英文摘要
Offline multi-objective optimization (MOO) seeks solutions with better objective trade-offs using only a fixed dataset, without querying the objectives. Diffusion models trained on such data have emerged as a promising approach, but their samples are not inherently better than the data and must be steered toward the Pareto front. Existing methods guide or condition every sampling step. We instead act on the initial noise and leave the sampling process unchanged. Across Off-MOO-Bench, we observe that the objectives, as functions of the noise, are sensitive to only a few directions. We estimate these directions once per task via a Recursive Feature Machine using function values alone, and a small cache serves every trade-off, so each candidate costs one noise displacement and one ODE solve. We prove that this displacement increases the learned scalarized objective in expectation, and that sweeping trade-offs recovers the flow's attainable front up to proxy and steering errors. With additional guidance, for which we introduce novel data-adaptive and Pareto-aware operators, our method attains the best average hypervolume rank among generative methods on 47 tasks, at comparable or lower sampling cost. Steering alone outranks the best prior generative method at a fraction of its sampling cost.
Comments65 pages, including appendices
