A Stochastic Gradient Method with an Exponential Convergence Rate for Finite Training Sets
Abstract¶
We propose a new stochastic gradient method for optimizing the sum of a finite set of smooth functions, where the sum is strongly convex. While standard stochastic gradient methods converge at sublinear rates for this problem, the proposed method incorporates a memory of previous gradient values in order to achieve a linear convergence rate. In a machine learning context, numerical experiments indicate that the new algorithm can dramatically outperform standard algorithms, both in terms of optimizing the training error and reducing the test error quickly.
Summary¶
Introduces the stochastic average gradient method, which stores the most recent gradient for each finite-sum component and averages those stored gradients to obtain a low-cost update with linear convergence on strongly convex objectives. It is one of the first modern variance-reduction methods showing that finite training sets permit faster rates than black-box stochastic gradient assumptions allow.