Finding Approximate Local Minima Faster than Gradient Descent
This addresses the computational bottleneck of training complex models like neural networks by providing a faster optimization method.
The paper introduces a second-order optimization algorithm that finds approximate local minima for non-convex problems, including neural network training, with linear time complexity in dimension and data size, which is faster than gradient descent's time to find critical points.
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.