Source code for "Sub-sampled Cubic Regularization for Non-convex Optimization", JM Kohler, A Lucchi, ICML 2017. https://arxiv.org/abs/1705.05933
Description
Python implementations of regularized Newton's methods for unconstrained continous (non- and convex) optimization. In particular we implement
a) The Trust Region framework as presented in Conn et al. 2000
b) The Adaptive Cubic Regularization (ARC) framework as presented in Cartis et al. 2011
c) The Subsampled Cubic Regularization (SCR) method presented in Kohler and Lucchi, 2017
You can pass any kind of continous objective (and derivatives) to these methods and choose between different common solvers for the quadratic models that are minimized in each step. In particular, a Krylov sub-space minimization routine based on the Lanczos process is available. This routine allows to escape strict saddle points efficiently.
Furthermore, these methods possess the best-known worst case iteration complexity bounds. Details regarding the convergence analysis and implementation of a sub-sampled cubic regularization method can be found in our ICML paper: https://arxiv.org/abs/1705.05933
Finally, for empirical risk minimization and similar objective involving loss function over datapoints, we offer the possibility of sub-sampling datapoints in each iteration according to different schemes.
