Adaptive hierarchical hyper-gradient descent
Renlong Jie, Junbin Gao, Andrey L. Vasnev, Minh‐Ngoc Tran · International Journal of Machine Learning and Cybernetics · 2022
Abstract Adaptive learning rate strategies can lead to faster convergence and better performance for deep learning models. There are some widely known human-designed adaptive optimizers such as Adam and RMSProp, gradient based adaptive methods such as hyper-descent and practical loss-based stepsize adaptation (L4), and meta learning approaches including learning to learn. However, the existing studies did not take into account the hierarchical structures of deep neural networks in designing the adaptation strategies. Meanwhile, the issue of balancing adaptiveness and convergence is still an open question to be answered. In this study, we investigate novel adaptive learning rate strategies at different levels based on the hyper-gradient descent framework and propose a method that adaptively learns the optimizer parameters by combining adaptive information at different levels. In addition, we show the relationship between regularizing over-parameterized learning rates and building combinations of adaptive learning rates at different levels. Moreover, two heuristics are introduced to guarantee the convergence of the proposed optimizers. 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 significantly outperform many baseline adaptive methods in a variety of circumstances.