Learning Linear Models Using Distributed Iterative Hessian Sketching

• URL: http://arxiv.org/abs/2112.04101v1
• Date: Wed, 8 Dec 2021 04:07:23 GMT
• Title: Learning Linear Models Using Distributed Iterative Hessian Sketching
• Authors: Han Wang and James Anderson
• Abstract summary: We consider the problem of learning the Markov parameters of a linear system from observed data. We show that a randomized and distributed Newton algorithm based on Hessian-sketching can produce $epsilon$-optimal solutions.
• Score: 4.567810220723372
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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.

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