Stochastic Optimization with Importance Sampling for Regularized Loss Minimization
published: Dec. 5, 2015, recorded: October 2015, views: 68
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Uniform sampling of training data has been commonly used in traditional stochastic optimization algorithms such as Proximal Stochastic Mirror Descent (prox-SMD) and Proximal Stochastic Dual Coordinate Ascent (prox-SDCA). Although uniform sampling can guarantee that the sampled stochastic quantity is an unbiased estimate of the corresponding true quantity, the resulting estimator may have a rather high variance, which negatively affects the convergence of the underlying optimization procedure. In this paper we study stochastic optimization, including prox-SMD and prox-SDCA, with importance sampling, which improves the convergence rate by reducing the stochastic variance. We theoretically analyze the algorithms and empirically validate their effectiveness.
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