Generalization as a robust performance property of learning-enabled dynamical systems
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.
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BibTeX
@misc{fabiani2026generalization,
title = {{Generalization as a robust performance property of learning-enabled dynamical systems}},
author = {Filippo Fabiani},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30431},
eprint = {2608.30431},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30431},
}
RIS
TY - UNPB
TI - Generalization as a robust performance property of learning-enabled dynamical systems
AU - Filippo Fabiani
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30431
UR - https://arxiv.org/abs/2608.30431
AB - 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.
ER -