发表机构
IMT School for Advanced Studies Lucca（卢cca高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将算法稳定性用于建立样本外界，为学习驱动动态系统的泛化性提供系统理论解释，建立矩阵不等式证明与稳定界，其结果适用于梯度下降、重球法等算法并可扩展至数据驱动控制，为验证比较学习动态泛化能力提供工具。
AI 中文摘要
通过将算法稳定性作为建立样本外界的手段，我们对数据驱动优化与反馈控制近似中产生的学习驱动动态系统的泛化性提供了系统理论层面的解释。给定两个相邻数据集，我们将样本替换建模为作用于灵敏度系统的外生扰动，同时通过积分二次约束编码数据依赖算子的增量行为。基于耗散性论证，我们建立了基于矩阵不等式的证明以及一致稳定性界，该界将学习到的算子的单样本灵敏度与依赖于算法的动态增益分离开来。后者可被优化，为验证和比较学习动态的泛化能力提供了可处理的工具。我们表明，该结果可恢复梯度下降的经典结果，自然适用于基于动量的方法如重球法和Nesterov加速，并可扩展至数据驱动控制领域。
英文摘要
By focusing on algorithmic stability as a means of establishing out-of-sample bounds, we provide a system-theoretic interpretation of generalization in learning-enabled dynamical systems arising in data-driven optimization and feedback control approximation. Given two neighboring datasets, we specifically model sample replacement as an exogenous disturbance acting on a sensitivity system, while the incremental behavior of the data-dependent operator is encoded through an integral quadratic constraint. By relying on dissipativity arguments, we establish a matrix inequality-based certificate and a uniform stability bound that separates the one-sample sensitivity of the learned operator, and an algorithm-dependent dynamical gain. The latter can then be optimized, offering a tractable tool for certifying and comparing generalization capabilities of learning dynamics. We show that our results recover classical ones for gradient descent, apply naturally to momentum-based methods such as heavy-ball and Nesterov acceleration, and extend to data-driven control.
