Before revision:  condition, PAGE can automatically switch to a faster linear convergence rate {\epsilon})} . Finally, we conduct several deep learning experiments (e.g., LeNet, VGG, ResNet) on real datasets in PyTorch , and the results demonstrate that PAGE not only converges much faster than SGD in training but also achieves the higher test accuracy, validating our theoretical results and confirming the practical superiority of PAGE.
After revision:  condition, PAGE can automatically switch to a faster linear convergence rate O(\cdot\log \frac{1{\epsilon})} . Finally, we conduct several deep learning experiments (e.g., LeNet, VGG, ResNet) on real datasets in PyTorch , and the results demonstrate that PAGE not only converges much faster than SGD in training but also achieves the higher test accuracy, validating our theoretical results and confirming the practical superiority of PAGE.