  Weight decay is a simple yet powerful regularization technique that has been
very widely used in training of deep neural networks (DNNs). While weight decay
has attracted much attention, previous studies fail to discover some overlooked
pitfalls on large gradient norms resulted by weight decay. In this paper, we
discover that, weight decay can unfortunately lead to large gradient norms at
the final phase (or the terminated solution) of training, which often indicates
bad convergence and poor generalization. To mitigate the gradient-norm-centered
pitfalls, we present the first practical scheduler for weight decay, called the
Scheduled Weight Decay (SWD) method that can dynamically adjust the weight
decay strength according to the gradient norm and significantly penalize large
gradient norms during training. Our experiments also support that SWD indeed
mitigates large gradient norms and often significantly outperforms the
conventional constant weight decay strategy for Adaptive Moment Estimation
(Adam).
