Variance Reduced Stochastic Gradient Descent with Neighbors
This work addresses computational bottlenecks in machine learning optimization, offering incremental improvements for faster training convergence.
The paper tackles the slow convergence of Stochastic Gradient Descent by proposing algorithms that use neighborhood structure in training data to share past stochastic gradients, improving transient optimization phases, with experimental results supporting the theory.
Stochastic Gradient Descent (SGD) is a workhorse in machine learning, yet its slow convergence can be a computational bottleneck. Variance reduction techniques such as SAG, SVRG and SAGA have been proposed to overcome this weakness, achieving linear convergence. However, these methods are either based on computations of full gradients at pivot points, or on keeping per data point corrections in memory. Therefore speed-ups relative to SGD may need a minimal number of epochs in order to materialize. This paper investigates algorithms that can exploit neighborhood structure in the training data to share and re-use information about past stochastic gradients across data points, which offers advantages in the transient optimization phase. As a side-product we provide a unified convergence analysis for a family of variance reduction algorithms, which we call memorization algorithms. We provide experimental results supporting our theory.