HVAdam: A Full-Dimension Adaptive Optimizer

Adaptive optimizers such as Adam and RMSProp have gained attraction in complex neural networks, including generative adversarial networks (GANs) and Transformers, thanks to their stable performance and fast convergence compared to non-adaptive optimizers. A frequently overlooked limitation of adaptive optimizers is that adjusting the learning rate of each dimension individually would ignore the knowledge of the whole loss landscape, resulting in slow updates of parameters, invalidating the learning rate adjustment strategy and eventually leading to widespread insufficient convergence of parameters. In this paper, we propose HVAdam, a novel optimizer that associates all dimensions of the parameters to find a new parameter update direction, leading to a refined parameter update strategy for an increased convergence rate. We validated HVAdam in extensive experiments, showing its faster convergence, higher accuracy, and more stable performance on image classification, image generation, and natural language processing tasks. Particularly, HVAdam achieves a significant improvement on GANs compared with other state-of-the-art methods, especially in Wasserstein-GAN (WGAN) and its improved version with gradient penalty (WGAN-GP). Code is available at https://github.com/ChihayaAnn/HVAdam .