  This work considers the problem of learning the Markov parameters of a linear
system from observed data. Recent non-asymptotic system identification results
have characterized the sample complexity of this problem in the single and
multi-rollout setting. In both instances, the number of samples required in
order to obtain acceptable estimates can produce optimization problems with an
intractably large number of decision variables for a second-order algorithm. We
show that a randomized and distributed Newton algorithm based on
Hessian-sketching can produce $\epsilon$-optimal solutions and converges
geometrically. Moreover, the algorithm is trivially parallelizable. Our results
hold for a variety of sketching matrices and we illustrate the theory with
numerical examples.
