Abstract
Abstract As a way to accelerate stochastic schemes, mini-batch optimization has been a popular choice for large scale learning due to its good general performance and ease of parallel computing. However, the performance of mini-batch algorithms can vary significantly based on the choice of the step size sequence, and, in general, there is a paucity of guidance for making good choices. In this paper, we propose to use the Barzilai–Borwein (BB) update step to automatically compute step sizes for the state of the art mini-batch method (mini-batch semi-stochastic gradient descent (mS2GD) method), thereby obtaining a new optimization method: mS2GD-BB. We prove that mS2GD-BB converges linearly in expectation for nonsmooth strongly convex objective functions. We analyze the complexity of mS2GD-BB and show that it achieves as fast a rate as modern stochastic gradient methods. Numerical experiments on standard data sets indicate that the performance of mS2GD-BB is superior to some state of the art methods.
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