Smoothing Proximal Gradient Method for General Structured Sparse Learning

TL;DR

This paper introduces a smoothing proximal gradient method for efficiently solving high-dimensional structured sparse regression problems with complex penalties, outperforming traditional methods in speed and scalability.

Contribution

It proposes a novel smoothing proximal gradient approach that handles non-separable structured penalties with improved convergence and scalability.

Findings

The method converges faster than standard first-order algorithms.

It is more scalable than interior-point methods.

Numerical experiments confirm efficiency and scalability.

Abstract

We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of such penalties as our motivating examples: 1) overlapping group lasso penalty, based on the l1/l2 mixed-norm penalty, and 2) graph-guided fusion penalty. For both types of penalties, due to their non-separability, developing an efficient optimization method has remained a challenging problem. In this paper, we propose a general optimization approach, called smoothing proximal gradient method, which can solve the structured sparse regression problems with a smooth convex loss and a wide spectrum of structured-sparsity-inducing penalties. Our approach is based on a general smoothing technique of Nesterov. It achieves a convergence rate faster than the standard first-order method, subgradient method, and is much more scalable than the most widely used interior-point method. Numerical results are reported to demonstrate the efficiency and scalability of the proposed method.