Descent Direction Stochastic Approximation Algorithm with Adaptive Step Sizes
Journal
Journal of Computational Mathematics
Date Issued
2019-06-01
Author(s)
Lužanin, Zorana
Kresoja, Milena
DOI
10.4208/jcm.1710-m2017-0021
Abstract
A stochastic approximation (SA) algorithm with new adaptive step sizes for solving
unconstrained minimization problems in noisy environment is proposed. New adaptive
step size scheme uses ordered statistics of fixed number of previous noisy function values
as a criterion for accepting good and rejecting bad steps. The scheme allows the algorithm to move in bigger steps and avoid steps proportional to 1/k when it is expected that
larger steps will improve the performance. An algorithm with the new adaptive scheme is
defined for a general descent direction. The almost sure convergence is established. The
performance of new algorithm is tested on a set of standard test problems and compared
with relevant algorithms. Numerical results support theoretical expectations and verify
efficiency of the algorithm regardless of chosen search direction and noise level. Numerical results on problems arising in machine learning are also presented. Linear regression
problem is considered using real data set. The results suggest that the proposed algorithm
shows promise.
unconstrained minimization problems in noisy environment is proposed. New adaptive
step size scheme uses ordered statistics of fixed number of previous noisy function values
as a criterion for accepting good and rejecting bad steps. The scheme allows the algorithm to move in bigger steps and avoid steps proportional to 1/k when it is expected that
larger steps will improve the performance. An algorithm with the new adaptive scheme is
defined for a general descent direction. The almost sure convergence is established. The
performance of new algorithm is tested on a set of standard test problems and compared
with relevant algorithms. Numerical results support theoretical expectations and verify
efficiency of the algorithm regardless of chosen search direction and noise level. Numerical results on problems arising in machine learning are also presented. Linear regression
problem is considered using real data set. The results suggest that the proposed algorithm
shows promise.