Abstract: We propose 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 accros various datasets and architecture choices. For example, our reformulation results in 20\% relative robustness improvement for CIFAR-100, and 10\% relative robustness improvement on CIFAR-10 comparing to the best tuned hyper-parameters of traditional weight decay resulting in models that have comparable performance to SOTA robustness methods. 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.