Adaptive Weight Decay: On The Fly Weight Decay Tuning for Improving Robustness

Amin Ghiasi, Ali Shafahi, Reza Ardekani

Keywords: weight decay, regularization, robust overfitting, adversarial robustness, noisy label, adversarial, pruning

TL;DR: We tune the hyper-parameter for weight decay during each iteration to stabilize training networks with smaller weight-norms which results in more robustness to adversarial examples and label noise, and less sensitivity to choices of learning rate.

Abstract: We introduce adaptive weight decay, which automatically tunes the hyper-parameter for weight decay during each training iteration. For classification problems, we propose changing the value of the weight-decay hyper-parameter on the fly based on the strength of updates from the classification loss (i.e., gradient of cross-entropy), and the regularization loss (i.e., $\ell_2$-norm of the weights). We show that this simple modification can result in large improvements in adversarial robustness — an area which suffers from robust overfitting — without requiring extra data. Specifically, our reformulation results in 20% relative robustness improvement for CIFAR-100, and 10% relative robustness improvement on CIFAR-10 comparing to traditional weight-decay. In addition, this method has other desirable properties, such as less sensitivity to learning rate, and smaller weight norms, which the latter contributes to robustness to overfitting to label noise, and pruning.

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