Better SGD using Second-order Momentum
This addresses the challenge of efficient optimization in deep learning by providing an adaptive method that improves convergence with decreasing gradient variance, though it is incremental as it builds on existing momentum and variance reduction techniques.
The paper tackles the problem of non-convex stochastic optimization by developing a new algorithm that uses Hessian-vector products to correct bias in SGD momentum, achieving an optimal $O(ε^{-3})$ complexity for finding an $ε$-critical point without requiring large batch sizes.
We develop a new algorithm for non-convex stochastic optimization that finds an $ε$-critical point in the optimal $O(ε^{-3})$ stochastic gradient and Hessian-vector product computations. Our algorithm uses Hessian-vector products to "correct" a bias term in the momentum of SGD with momentum. This leads to better gradient estimates in a manner analogous to variance reduction methods. In contrast to prior work, we do not require excessively large batch sizes, and are able to provide an adaptive algorithm whose convergence rate automatically improves with decreasing variance in the gradient estimates. We validate our results on a variety of large-scale deep learning architectures and benchmarks tasks.