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. A further improvement is achieved by interleaving GCG with fixed-rank local subspace optimization. A series of experiments on matrix completion, multi-class classification, multi-view dictionary learning and overlapping group lasso shows that the proposed method can significantly reduce the training cost of current alternatives.

本文研究了广义条件梯度算法在解决稀疏结构优化问题中的应用，提出了优化极化算子计算的高效方法，证明其在数据处理方面的有效性。实验表明，该算法能够显著减少现有方法的训练成本。

稀疏估计的广义条件梯度算法