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arXiv · 1912.00858

Efficient Relaxed Gradient Support Pursuit for Sparsity Constrained Non-convex Optimization

Fanhua Shang·Bingkun Wei·Hongying Liu·Yuanyuan Liu·Jiacheng Zhuo
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Abstract

Large-scale non-convex sparsity-constrained problems have recently gained extensive attention. Most existing deterministic optimization methods (e.g., GraSP) are not suitable for large-scale and high-dimensional problems, and thus stochastic optimization methods with hard thresholding (e.g., SVRGHT) become more attractive. Inspired by GraSP, this paper proposes a new general relaxed gradient support pursuit (RGraSP) framework, in which the sub-algorithm only requires to satisfy a slack descent condition. We also design two specific semi-stochastic gradient hard thresholding algorithms. In particular, our algorithms have much less hard thresholding operations than SVRGHT, and their average per-iteration cost is much lower (i.e., O(d) vs. O(d log(d)) for SVRGHT), which leads to faster convergence. Our experimental results on both synthetic and real-world datasets show that our algorithms are superior to the state-of-the-art gradient hard thresholding methods.

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Fanhua Shang, Bingkun Wei, Hongying Liu, Yuanyuan Liu, Jiacheng Zhuo. 2019-12-02. Efficient Relaxed Gradient Support Pursuit for Sparsity Constrained Non-convex Optimization. https://arxiv.org/abs/1912.00858

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