Title: Blockwise Adaptivity:  Faster Training and Better Generalization in Deep Learning. Abstract: Stochastic methods with coordinate-wise adaptive stepsize (such as RMSprop and Adam) have been widely used in training deep neural networks. Despite their fast convergence, they can generalize worse than stochastic gradient descent.  In this paper, by revisiting the design of Adagrad, we propose to split the network parameters into blocks, and use a blockwise
adaptive stepsize. Intuitively, blockwise adaptivity is less aggressive than adaptivity to individual coordinates, and can have a better balance between adaptivity and generalization. We show theoretically that the proposed blockwise adaptive gradient
descent has comparable regret in online convex learning and convergence rate for optimizing nonconvex objective as its counterpart with coordinate-wise adaptive stepsize, but is better up to some constant. We also study its uniform stability 
and show that blockwise adaptivity can lead to lower generalization error than coordinate-wise adaptivity. Experimental results show that blockwise adaptive gradient descent converges faster and improves generalization performance over Nesterov's accelerated gradient and Adam.