Title: Adaptive Hierarchical Hyper-gradient Descent. Abstract: Adaptive learning rates can lead to faster convergence and better final performance
for deep learning models. There are several widely known human-designed adap-
tive optimizers such as Adam and RMSProp,  gradient based adaptive methods
such as hyper-descent and L4, and meta learning approaches including learning
to learn. However, the issue of balancing adaptiveness and over-parameterization
is still a topic to be addressed.   In this study,  we investigate different levels of
learning rate adaptation based on the framework of hyper-gradient descent, and
further propose a method that adaptively learns the model parameters for combin-
ing different levels of adaptations. Meanwhile, we show the relationship between
adding regularization on over-parameterized learning rates and building combi-
nations of different levels of adaptive learning rates.  The experiments on several
network architectures including feed-forward networks, LeNet-5 and ResNet-18/34
show  that  the  proposed  multi-level  adaptive  approach  can  outperform  baseline
adaptive methods in a variety circumstances with statistical significance.