这篇论文教你怎么用求解器的中间迭代步骤来多搞训练数据，还给了理论分析并连接到GLENS方法，做优化或生成模型的人可以看看。
本文针对参数优化问题中数据稀缺的挑战，提出了一种k-邻域数据收集策略，通过将收敛解与中间求解器迭代结合来扩充训练数据。作者推导了基于Rademacher复杂度的泛化界，揭示了k-邻域及相关参数的作用。方法聚焦于由投影梯度下降求解的单侧盒约束二次规划，并通过两个示例展示了求解器行为。该研究提升了DDDAS范式中数据-模型-优化循环的效率。最后讨论了学习求解器迭代数据的两种观点，并将其与GLENS全局搜索方法关联。
Complexity Bounds and Approaches to Learning Projected Gradient Descent Solver Iterates
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.