In this paper we explore acceleration techniques for large scale nonconvex optimization problems with special focuses on deep neural networks. The extrapolation scheme is a classical approach for accelerating stochastic gradient descent for convex optimization, but it does not work well for nonconvex optimization typically. Alternatively, we propose an interpolation scheme to accelerate nonconvex optimization and call the method Interpolatron. We explain motivation behind Interpolatron and conduct a thorough empirical analysis. Empirical results on DNNs of great depths (e.g., 98-layer ResNet and 200-layer ResNet) on CIFAR-10 and ImageNet show that Interpolatron can converge much faster than the state-of-the-art methods such as the SGD with momentum and Adam. Furthermore, Anderson's acceleration, in which mixing coefficients are computed by least-squares estimation, can also be used to improve the performance. Both Interpolatron and Anderson's acceleration are easy to implement and tune. We also show that Interpolatron has linear convergence rate under certain regularity assumptions.

"How does depth help?" is a fundamental question in the theory of deep learning. Conventional wisdom, backed by theoretical studies (e.g. Eldan & Shamir 2016; Raghu et al. 2017; Lee et al. 2017; Cohen et al. 2016; Daniely 2017), holds that adding layers increases expressive power. But often this expressive gain comes at a price –optimization is harder for deeper networks (viz., vanishing/exploding gradients). Recent works on "landscape characterization" implicitly adopt this worldview (e.g.