Generalized Conditional Gradient for Sparse Estimation

Understand

Structured sparsity is an important modeling tool that expands the applicability of convex formulations for data analysis, however it also creates significant challenges for efficient algorithm design.

• In this paper we investigate the generalized conditional gradient (GCG) algorithm for solving structured sparse optimization problems---demonstrating that, with some enhancements, it can provide a more efficient alternative to current state of the art approaches.
• After providing a comprehensive overview of the convergence properties of GCG, we develop efficient methods for evaluating polar operators, a subroutine that is required in each GCG iteration.
• In particular, we show how the polar operator can be efficiently evaluated in two important scenarios: dictionary learning and structured sparse estimation.