Generalization as a robust performance property of learning-enabled dynamical systems

2026-08-31

AI Summary

本文通过算法稳定性建立样本外边界，利用耗散性论点为学习动力系统提供了一种系统理论解释，并通过优化算法依赖的动力增益来认证和比较学习动态的泛化能力。

Abstract

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.

Problem

• generalization
• learning-enabled dynamical systems
• algorithmic stability
• out-of-sample bounds
• data-driven optimization

Innovation

• algorithmic stability
• integral quadratic constraint
• dissipativity arguments
• matrix inequality-based certificate
• generalization capabilities