This work is a part of ICLR Reproducibility Challenge 2019, we try to reproduce the results in the conference submission PADAM: Closing The Generalization Gap of Adaptive Gradient Methods In Training Deep Neural Networks. Adaptive gradient methods proposed in past demonstrate a degraded generalization performance than the stochastic gradient descent (SGD) with momentum. The authors try to address this problem by designing a new optimization algorithm that bridges the gap between the space of Adaptive Gradient algorithms and SGD with momentum. With this method a new tunable hyperparameter called partially adaptive parameter p is introduced that varies between [0, 0.5]. We build the proposed optimizer and use it to mirror the experiments performed by the authors. We review and comment on the empirical analysis performed by the authors. Finally, we also propose a future direction for further study of Padam. Our code is available at: https://github.com/yashkant/Padam-Tensorflow

Stochastic gradient descent (SGD) (Robbins and Monro, 1951) and its variants have been widely used in training deep neural networks. Among those variants, adaptive gradient methods (AdaGrad) (Duchi et al., 2011; McMahan and Streeter, 2010), which scale each coordinate of the gradient by a function of past gradients, can achieve better performance than vanilla SGD in practice when the gradients are sparse. An intuitive explanation for the success of AdaGrad is that it automatically adjusts the learning rate for each feature based on the partial gradient, which accelerates the convergence. However, AdaGrad was later found to demonstrate degraded performance especially in cases where the loss function is nonconvex or the gradient is dense, due to rapid decay of learning rate.

Adaptive gradient methods, which adopt historical gradient information to automatically adjust the learning rate, have been observed to generalize worse than stochastic gradient descent (SGD) with momentum in training deep neural networks. This leaves how to close the generalization gap of adaptive gradient methods an open problem. In this work, we show that adaptive gradient methods such as Adam, Amsgrad, are sometimes "over adapted". We design a new algorithm, called Partially adaptive momentum estimation method (Padam), which unifies the Adam/Amsgrad with SGD to achieve the best from both worlds. Experiments on standard benchmarks show that Padam can maintain fast convergence rate as Adam/Amsgrad while generalizing as well as SGD in training deep neural networks. These results would suggest practitioners pick up adaptive gradient methods once again for faster training of deep neural networks.