Learning of Linear Dynamical Systems as a Non-Commutative Polynomial Optimization Problem
This addresses the challenge of estimating system matrices in linear dynamical systems, which is an incremental improvement in proper learning methods.
The paper tackles the proper learning of linear dynamical systems by formulating it as a non-commutative polynomial optimization problem, guaranteeing global convergence to a least-squares estimator despite non-convexity, with promising computational results.
There has been much recent progress in forecasting the next observation of a linear dynamical system (LDS), which is known as the improper learning, as well as in the estimation of its system matrices, which is known as the proper learning of LDS. We present an approach to proper learning of LDS, which in spite of the non-convexity of the problem, guarantees global convergence of numerical solutions to a least-squares estimator. We present promising computational results.