Finding Approximate Local Minima Faster than Gradient Descent
Optimization and Control
2017-04-26 v4 Data Structures and Algorithms
Neural and Evolutionary Computing
Machine Learning
Abstract
We design a non-convex second-order optimization algorithm that is guaranteed to return an approximate local minimum in time which scales linearly in the underlying dimension and the number of training examples. The time complexity of our algorithm to find an approximate local minimum is even faster than that of gradient descent to find a critical point. Our algorithm applies to a general class of optimization problems including training a neural network and other non-convex objectives arising in machine learning.
Cite
@article{arxiv.1611.01146,
title = {Finding Approximate Local Minima Faster than Gradient Descent},
author = {Naman Agarwal and Zeyuan Allen-Zhu and Brian Bullins and Elad Hazan and Tengyu Ma},
journal= {arXiv preprint arXiv:1611.01146},
year = {2017}
}