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Stochastic approximation is one of the effective approach to deal with thelarge-scale machine learning problems and the recent research has focused onreduction of variance, caused by the noisy approximations of the gradients. Inthis paper, we have proposed novel variants of SAAG-I and II (StochasticAverage Adjusted Gradient) (Chauhan et al. 2017), called SAAG-III and IV,respectively. Unlike SAAG-I, starting point is set to average of previous epochin SAAG-III, and unlike SAAG-II, the snap point and starting point are set toaverage and last iterate of previous epoch in SAAG-IV, respectively. Todetermine the step size, we have used Stochastic Backtracking-Armijo lineSearch (SBAS) which performs line search only on selected mini-batch of datapoints. Since backtracking line search is not suitable for large-scale problemsand the constants used to find the step size, like Lipschitz constant, are notalways available so SBAS could be very effective in such cases. We haveextended SAAGs (I, II, III and IV) to solve non-smooth problems and designedtwo update rules for smooth and non-smooth problems. Moreover, our theoreticalresults have proved linear convergence of SAAG-IV for all the four combinationsof smoothness and strong-convexity, in expectation. Finally, our experimentalstudies have proved the efficacy of proposed methods against the state-of-arttechniques.

SAAGs: Biased Stochastic Variance Reduction Methods for Large-scale Learning