225 research outputs found
Variance Reduced Stochastic Gradient Descent with Neighbors
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.Comment: Appears in: Advances in Neural Information Processing Systems 28
(NIPS 2015). 13 page
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