Accelerated Block Coordinate Proximal Gradients with Applications in High Dimensional Statistics
This work addresses optimization challenges in high-dimensional statistics, offering incremental improvements for researchers in signal processing and machine learning.
The paper tackles nonconvex optimization problems by proposing a novel variant of the accelerated proximal gradient method that uses adaptive momentum and block coordinate updates, achieving provable local linear convergence in applications like sparse linear regression with various regularizations.
Nonconvex optimization problems arise in different research fields and arouse lots of attention in signal processing, statistics and machine learning. In this work, we explore the accelerated proximal gradient method and some of its variants which have been shown to converge under nonconvex context recently. We show that a novel variant proposed here, which exploits adaptive momentum and block coordinate update with specific update rules, further improves the performance of a broad class of nonconvex problems. In applications to sparse linear regression with regularizations like Lasso, grouped Lasso, capped $\ell_1$ and SCAP, the proposed scheme enjoys provable local linear convergence, with experimental justification.