- Keywords: optimization, deep learning, blockwise adaptivity
- TL;DR: We propose a blockwise adaptive gradient descent method that enjoys faster convergence and better generalization than its coordinate-wise counterpart.
- 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.