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

TL;DR

This paper introduces a new relaxed gradient support pursuit framework for large-scale non-convex sparsity problems, featuring semi-stochastic algorithms with reduced thresholding operations and faster convergence, outperforming existing methods.

Contribution

It proposes a novel RGraSP framework and two semi-stochastic algorithms that require fewer thresholding steps and have lower per-iteration costs, improving efficiency over prior methods.

Findings

Algorithms outperform state-of-the-art methods on synthetic datasets.

Reduced thresholding operations lead to faster convergence.

Experimental results demonstrate superior efficiency and accuracy.

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.