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

• URL: http://arxiv.org/abs/2608.30431v1
• Date: Mon, 31 Aug 2026 08:25:50 GMT
• Title: Generalization as a robust performance property of learning-enabled dynamical systems
• Abstract summary: We provide a system-theoretic interpretation of generalization in learning-enabled dynamical systems.<n>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.
• Score: 0.45687771576879593
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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