Fast sparse optimization via adaptive shrinkage

Vito Cerone; Sophie M. Fosson; Diego Regruto

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arXiv · 2501.12236

Fast sparse optimization via adaptive shrinkage

Vito Cerone·Sophie M. Fosson·Diego Regruto

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Abstract

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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BibTeX RIS

Vito Cerone, Sophie M. Fosson, Diego Regruto. 2025-01-21. Fast sparse optimization via adaptive shrinkage. https://arxiv.org/abs/2501.12236

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