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Tail bounds for stochastic approximation

Michael P. Friedlander(mpf***at***cs.ubc.ca)
Gabriel Goh(ggoh***at***cs.ubc.ca)

Abstract: Stochastic-approximation gradient methods are attractive for large-scale convex optimization because they offer inexpensive iterations. They are especially popular in data-fitting and machine-learning applications where the data arrives in a continuous stream, or it is necessary to minimize large sums of functions. It is known that by appropriately decreasing the variance of the error at each iteration, the expected rate of convergence matches that of the underlying deterministic gradient method. Here we give conditions under which this happens with overwhelming probability.

Keywords: stochastic approximation, sample-average approximation, incremental gradient, convex optimization

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Stochastic Programming

Citation: Department of Computer Science, University of British Columbia, April 2013

Download: [PDF]

Entry Submitted: 04/19/2013
Entry Accepted: 04/19/2013
Entry Last Modified: 04/19/2013

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