  Stochastic approximation is one of the effective approach to deal with the
large-scale machine learning problems and the recent research has focused on
reduction of variance, caused by the noisy approximations of the gradients. In
this paper, we have proposed novel variants of SAAG-I and II (Stochastic
Average Adjusted Gradient) (Chauhan et al. 2017), called SAAG-III and IV,
respectively. Unlike SAAG-I, starting point is set to average of previous epoch
in SAAG-III, and unlike SAAG-II, the snap point and starting point are set to
average and last iterate of previous epoch in SAAG-IV, respectively. To
determine the step size, we have used Stochastic Backtracking-Armijo line
Search (SBAS) which performs line search only on selected mini-batch of data
points. Since backtracking line search is not suitable for large-scale problems
and the constants used to find the step size, like Lipschitz constant, are not
always available so SBAS could be very effective in such cases. We have
extended SAAGs (I, II, III and IV) to solve non-smooth problems and designed
two update rules for smooth and non-smooth problems. Moreover, our theoretical
results have proved linear convergence of SAAG-IV for all the four combinations
of smoothness and strong-convexity, in expectation. Finally, our experimental
studies have proved the efficacy of proposed methods against the state-of-art
techniques.
