Theoretical Analysis of Sparse Optimization with Reparameterization, Weight Decay, and Adaptive Learning Rate
Institute of Computing Technology,Chinese Academy of Sciences · Tsinghua University, Tsinghua University · Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences · Shanghai University of Finance and Economics
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摘要
Sparse optimization is a fundamental challenge in various practical applications. A popular approach to sparse optimization is Lp 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 lp-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 L1-regularization approach while preserving test accuracy.