Robust System Identification: Finite-sample Guarantees and Connection to Regularization
Keywords: dynamical system, time series, system identification, optimization
Abstract: We consider the problem of learning nonlinear dynamical systems from a single sample trajectory. While the least squares estimate (LSE) is commonly used for this task, it suffers from poor identification errors when the sample size is small or the model fails to capture the system's true dynamics. To overcome these limitations, we propose a robust LSE framework, which incorporates robust optimization techniques, and prove that it is equivalent to regularizing LSE using general Schatten $p$-norms. We provide non-asymptotic performance guarantees for linear systems, achieving an error rate of $\widetilde{\mathcal{O}}(1/\sqrt{T})$, and show that it avoids the curse of dimensionality, unlike state-of-the-art Wasserstein robust optimization models. Empirical results demonstrate substantial improvements in real-world system identification and online control tasks, outperforming existing methods.
Primary Area: learning on time series and dynamical systems
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Submission Number: 8419
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