发表机构
Research Institute for Interdisciplinary Sciences, School of Information Management and Engineering, Shanghai University of Finance and Economics; Department of Decision Analytics and Operations, City University of Hong Kong; Department of Industrial and Systems Engineering, University of Minnesota（上海财经大学信息管理与工程学院交叉科学研究院; 香港城市大学决策分析与运营学系; 明尼苏达大学工业与系统工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出统一框架，解释先学习后微分（LTD）梯度估计方法的原理与精度保证，涵盖多种回归与神经网络，为跨方法分析提供共同基础。
AI 中文摘要
先学习后微分（LTD）方法通过将模型拟合到模拟输出并对其微分来估计梯度。我们开发了一个统一框架，用以解释LTD微分的内容及其估计梯度的准确性。对于具有加权表示的模型，LTD微分的是底层概率测度的学习表示。随后，我们展示了拟合模型的精度保证如何转化为梯度及高阶导数的保证，在适当的光滑性条件下，其收敛速率接近标准蒙特卡洛速率。该框架涵盖了核回归、局部多项式回归和核岭回归的已有结果，并为多核学习和光滑神经网络提供了进一步的保证。这些结果为跨学习方法理解和分析LTD提供了共同基础。
英文摘要
Learn-then-differentiate (LTD) estimates gradients by fitting a model to simulation outputs and differentiating it. We develop a unified framework explaining what LTD differentiates and how accurately it estimates gradients. For models with a weighted representation, LTD differentiates a learned representation of the underlying probability measure. We then show how accuracy guarantees for fitted models translate into guarantees for gradients and higher-order derivatives, with rates approaching the standard Monte Carlo rate under suitable smoothness conditions. The framework recovers established results for kernel regression, local polynomial regression, and kernel ridge regression, and yields further guarantees for multiple kernel learning and smooth neural networks. These results provide a common foundation for understanding and analyzing LTD across learning methods.
