Learning Linear Systems under Heavy-Tailed Noise: A Non-Asymptotic Analysis from A Single Trajectory
The paper analyzes estimating parameters of linear systems from a single trajectory when noise has heavy tails. It provides non-asymptotic bounds showing that if the noise has a bounded pth moment greater than two, model-based estimation remains statistically viable, though convergence slows down by a factor related to T^(1/p). This is crucial for real-world control where heavy disturbances are common.