Correcting Momentum with Second-order Information

• URL: http://arxiv.org/abs/2103.03265v1
• Date: Thu, 4 Mar 2021 19:01:20 GMT
• Title: Correcting Momentum with Second-order Information
• Authors: Hoang Tran, Ashok Cutkosky
• Abstract summary: We develop a new algorithm for non-critical optimization that finds an $O(epsilon)$epsilon point in the optimal product. We validate our results on a variety of large-scale deep learning benchmarks and architectures.
• Score: 50.992629498861724
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a new algorithm for non-convex stochastic optimization that finds an $\epsilon$-critical point in the optimal $O(\epsilon^{-3})$ 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 (or indeed any restrictions at all on the batch size), and both our algorithm and its analysis are much simpler. We validate our results on a variety of large-scale deep learning benchmarks and architectures, where we see improvements over SGD and Adam.

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