提出自适应收缩的快速稀疏优化方法，收敛更快且保持简单易实现。
Fast sparse optimization via adaptive shrinkage
- 基于对数正则化设计自适应收缩参数的近端算法
- 实验表明收敛速度显著优于现有主流算法
- 适合需要快速求解大规模稀疏问题的研究者
随着高维数据驱动问题和时变系统追踪需求的增长，快速稀疏优化变得愈发重要。在线性稀疏优化框架中，迭代收缩阈值算法（ISTA）是求解Lasso问题的有效方法，因其易于实现而广受青睐，但其收敛速度较慢。本文提出一种基于对数正则化的近端方法，该方法本质上是一种具有自适应收缩超参数的迭代收缩阈值算法。这种自适应机制显著改善了算法轨迹，实现了更快的收敛速度，同时保持了原始方法的简洁性。本文贡献包含两方面：一是推导并分析所提算法；二是通过数值实验验证其快速收敛性，并与当前先进算法性能进行对比分析。
原文摘要 · Abstract (English)
The need for fast sparse optimization is emerging, e.g., to deal with large-dimensional data-driven problems and to track time-varying systems. In the framework of linear sparse optimization, the iterative shrinkage-thresholding algorithm is a valuable method to solve Lasso, which is particularly appreciated for its ease of implementation. Nevertheless, it converges slowly. In this paper, we develop a proximal method, based on logarithmic regularization, which turns out to be an iterative shrinkage-thresholding algorithm with adaptive shrinkage hyperparameter. This adaptivity substantially enhances the trajectory of the algorithm, in a way that yields faster convergence, while keeping the simplicity of the original method. Our contribution is twofold: on the one hand, we derive and analyze the proposed algorithm; on the other hand, we validate its fast convergence via numerical experiments and we discuss the performance with respect to state-of-the-art algorithms.
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