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This paper introduces an active learning algorithm for linear system identification that uses optimally centered noise excitation to minimize sample complexity. They derive lower bounds on sample complexity for any active learning algorithm and then prove that their proposed algorithm, based on ordinary least squares and semidefinite programming, achieves a matching upper bound, up to universal factors. The resulting tight bounds explicitly show the dependence on system parameters like state dimension, providing a practical guide for system identification.
Achieving minimal sample complexity in linear system identification is now possible with an efficiently computable algorithm based on ordinary least squares and semidefinite programming.
We propose an active learning algorithm for linear system identification with optimal centered noise excitation. Notably, our algorithm, based on ordinary least squares and semidefinite programming, attains the minimal sample complexity while allowing for efficient computation of an estimate of a system matrix. More specifically, we first establish lower bounds of the sample complexity for any active learning algorithm to attain the prescribed accuracy and confidence levels. Next, we derive a sample complexity upper bound of the proposed algorithm, which matches the lower bound for any algorithm up to universal factors. Our tight bounds are easy to interpret and explicitly show their dependence on the system parameters such as the state dimension.