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This paper establishes a system-theoretic framework for certifying generalization in learning-enabled dynamical systems by modeling dataset perturbations as exogenous disturbances. By leveraging dissipativity arguments, the authors derive matrix inequality certificates that separate sample sensitivity from algorithm-dependent gains, offering a tractable method to optimize and compare dynamics across gradient descent and momentum-based methods like heavy-ball. These results bridge classical control theory with machine learning optimization, providing rigorous bounds for data-driven control applications.
Generalization as a robust performance property of learning-enabled dynamical systems
arXiv:2608.30431v1 Announce Type: cross 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.
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.
Systems and Control (eess.SY); Machine Learning (cs.LG); Optimization and Control (math.OC)
arXiv:2608.30431 [eess.SY]
(or arXiv:2608.30431v1 [eess.SY] for this version)
https://doi.org/10.48550/arXiv.2608.30431 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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