发表机构
Princeton University（普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对数据稀缺挑战，研究用k邻域数据收集策略扩充训练数据，推导泛化界，以投影梯度下降求解单边盒约束二次规划为例说明，提高数据-模型-优化循环效率，实现更强大的DDDAS范式，并与GLENS联系。
AI 中文摘要
数据稀缺在训练生成模型以产生参数优化问题的初始猜测时构成了一个基本挑战，这些问题在数值上求解成本高昂。因此，我们研究了一种k邻域数据收集策略，该策略用中间求解器迭代来扩充收敛解的数据集，在不进行额外求解器运行的情况下增加训练数据量。为理解此方法的益处，我们基于拉德马赫复杂度推导了一个泛化界，揭示了k邻域和相关参数的作用。我们专注于通过投影梯度下降求解的单边盒约束二次规划。在两个例子中说明了该求解器的行为。本文提出的方法通过提高数据-模型-优化循环的效率实现了更强大的DDDAS范式。最后讨论了学习求解器迭代数据的两种观点，并将我们的分析与一种新的数据高效全局搜索方法GLENS联系起来。
英文摘要
Data scarcity poses a fundamental challenge in training generative models to produce initial guesses for parametric optimization problems that are otherwise numerically expensive to solve. We therefore study a $k$-neighborhood data collection strategy that augments datasets of converged solutions with intermediate solver iterates, increasing the amount of training data without additional solver runs. To understand the benefits of this approach, we derive a generalization bound based on Rademacher complexity that reveals the role of the $k$-neighborhoods and related parameters. To achieve this result, we focus on one-sided box-constrained quadratic programs solved by projected gradient descent. We illustrate the behavior of this solver on two examples. The approach proposed in this paper enables a more capable DDDAS paradigm by improving the efficiency of the data-model-optimization loop. We finish by discussing two views of learning solver-iterate data and connect our analysis with GLENS, a new data-efficient global search method.
