  Adaptive gradient methods, which adopt historical gradient information to
automatically adjust the learning rate, despite the nice property of fast
convergence, 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, which unifies the Adam/Amsgrad with SGD by
introducing a partial adaptive parameter $p$, to achieve the best from both
worlds. We also prove the convergence rate of our proposed algorithm to a
stationary point in the stochastic nonconvex optimization setting. Experiments
on standard benchmarks show that our proposed algorithm can maintain a 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.
