Smoothing Proximal Gradient Method for General Structured Sparse Learning
This work addresses optimization bottlenecks for researchers and practitioners in machine learning dealing with structured sparse learning, though it is incremental as it builds on existing smoothing techniques.
The paper tackles the challenge of efficiently optimizing high-dimensional regression models with structured-sparsity-inducing penalties, such as overlapping group lasso and graph-guided fusion, by proposing a smoothing proximal gradient method. The result is a method that achieves a faster convergence rate than standard first-order methods and is more scalable than interior-point methods, as demonstrated by numerical results.
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.