English

Theoretical Analysis of Sparse Optimization with Reparameterization, Weight Decay, and Adaptive Learning Rate

Machine Learning 2026-05-29 v2 Artificial Intelligence

Abstract

Sparse optimization is a fundamental challenge in various practical applications. A popular approach to sparse optimization is p\ell_p regularization. However, it may encounter optimization instability due to the unbounded gradients when 0<p<10<p<1. In this paper, we introduce a novel approach to sparse optimization termed ReWA, based on Reparameterization, Weight decay, and Adaptive learning rate. ReWA is closely connected to p\ell_p-regularization, yet it unveils a distinct optimization landscape that helps mitigate instability issues. Experiments on CIFAR-10 and ImageNet with ResNets demonstrate that ReWA leads to significant sparsity improvements over the 1\ell_1-regularization approach while preserving test accuracy.

Keywords

Cite

@article{arxiv.2605.25134,
  title  = {Theoretical Analysis of Sparse Optimization with Reparameterization, Weight Decay, and Adaptive Learning Rate},
  author = {Huangyu Xu and Jingqin Yang and Qianqian Xu and Jiaye Teng},
  journal= {arXiv preprint arXiv:2605.25134},
  year   = {2026}
}

Comments

31 pages, 5 figures. Submitted to ICML 2026