Boosting-Enabled Robust System Identification of Partially Observed LTI Systems Under Heavy-Tailed Noise
Vinay Kanakeri, Aritra Mitra
TL;DR
The work addresses identifying parameters of partially observed LTI systems under heavy-tailed noise that only has finite second moments. It introduces a robust boosting-based algorithm that partitions data into buckets, computes bucket-wise estimates, and aggregates them with the geometric median to achieve concentration. A main finite-sample result shows a bound of the form ||hatG−G|| ≤ ((σv C1+σw C2)/σu) sqrt( p log(1/δ) / N ) under certain K and M, achieving logarithmic dependence on δ, and the analysis relies on Markov bounds with the geometric median rather than Chernoff-type bounds. This extends non-asymptotic system identification to heavy-tailed, partially observed settings, enabling data-driven control under non-ideal noise.
Abstract
We consider the problem of system identification of partially observed linear time-invariant (LTI) systems. Given input-output data, we provide non-asymptotic guarantees for identifying the system parameters under general heavy-tailed noise processes. Unlike previous works that assume Gaussian or sub-Gaussian noise, we consider significantly broader noise distributions that are required to admit only up to the second moment. For this setting, we leverage tools from robust statistics to propose a novel system identification algorithm that exploits the idea of boosting. Despite the much weaker noise assumptions, we show that our proposed algorithm achieves sample complexity bounds that nearly match those derived under sub-Gaussian noise. In particular, we establish that our bounds retain a logarithmic dependence on the prescribed failure probability. Interestingly, we show that such bounds can be achieved by requiring just a finite fourth moment on the excitatory input process.