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

Sparse optimization is a fundamental challenge in various practical applications. A popular approach to sparse optimization is ℓ p regularization. However, it may encounter optimization instability due to the unbounded gradients when 0 < 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 ℓ 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 ℓ 1 -regularization approach while preserving test accuracy.