Title: GENERALIZED ADAPTIVE MOMENT ESTIMATION. Abstract: Adaptive gradient methods have experienced great success in training deep neural networks (DNNs). The basic idea of the methods is to track and properly make use of the first and/or second moments of the gradient for model-parameter updates over iterations for the purpose of removing the need for manual interference. In this work, we propose a new adaptive gradient method, referred to as generalized adaptive moment estimation (Game). From a high level perspective, the new method introduces two more parameters w.r.t. AMSGrad (S. J. Reddi & Kumar (2018)) and one more parameter w.r.t. PAdam (Chen & Gu (2018)) to enlarge the parameter- selection space for performance enhancement while reducing the memory cost per iteration compared to AMSGrad and PAdam. The saved memory space amounts to the number of model parameters, which is significant for large-scale DNNs. Our motivation for introducing additional parameters in Game is to provide algorithmic flexibility to facilitate a reduction of the performance gap between training and validation datasets when training a DNN. Convergence analysis is provided for applying Game to solve both convex optimization and smooth nonconvex optmization. Empirical studies for training four convolutional neural networks over MNIST and CIFAR10 show that under proper parameter selection, Game produces promising validation performance as compared to AMSGrad and PAdam.