Approximate Regularization Paths for Nuclear Norm Minimization Using Singular Value Bounds -- With Implementation and Extended Appendix
For practitioners using nuclear norm minimization, this work reduces the computational burden of tuning the regularization parameter, but the extension is incremental.
The authors extend a method for approximating the regularization path in nuclear norm minimization, providing error bounds for singular values, and demonstrate it on large-scale model order reduction benchmarks.
The widely used nuclear norm heuristic for rank minimization problems introduces a regularization parameter which is difficult to tune. We have recently proposed a method to approximate the regularization path, i.e., the optimal solution as a function of the parameter, which requires solving the problem only for a sparse set of points. In this paper, we extend the algorithm to provide error bounds for the singular values of the approximation. We exemplify the algorithms on large scale benchmark examples in model order reduction. Here, the order of a dynamical system is reduced by means of constrained minimization of the nuclear norm of a Hankel matrix.