Fast sparse optimization via adaptive shrinkage

• URL: http://arxiv.org/abs/2501.12236v1
• Date: Tue, 21 Jan 2025 15:58:21 GMT
• Title: Fast sparse optimization via adaptive shrinkage
• Authors: Vito Cerone, Sophie M. Fosson, Diego Regruto,
• Abstract summary: We develop a proximal method, based on logarithmic regularization, which turns out to be an iterative shrinkage-thresholding algorithm. This adaptivity substantially enhances the trajectory of the algorithm, in a way that yields faster convergence. We validate its fast convergence via numerical experiments and we discuss the performance with respect to state-of-the-art algorithms.
• Score: 0.6226609932118122
• License:
• 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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