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2016

Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm

4 years 3 months ago
Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm
We improve a recent guarantee of Bach and Moulines on the linear convergence of SGD for smooth and strongly convex objectives, reducing a quadratic dependence on the strong convexity to a linear dependence. Furthermore, we show how reweighting the sampling distribution (i.e. importance sampling) is necessary in order to further improve convergence, and obtain a linear dependence on average smoothness, dominating previous results, and more broadly discus how importance sampling for SGD can improve convergence also in other scenarios. Our results are based on a connection between SGD and the randomized Kaczmarz algorithm, which allows us to transfer ideas between the separate bodies of literature studying each of the two methods.
Deanna Needell, Nathan Srebro, Rachel Ward
Added 08 Apr 2016
Updated 08 Apr 2016
Type Journal
Year 2016
Where MP
Authors Deanna Needell, Nathan Srebro, Rachel Ward
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