Subject: Unconstrained optimization
Subject: Stochastic optimization
Subject: Stochastic approximation
Subject: Noisy function
Subject: Adaptive step size
Subject: Descent direction
Subject: Linear regression model
Year: 2019
Type: Journal Article
Title: Descent Direction Stochastic Approximation Algorithm with Adaptive Step Sizes
Author: Lužanin, Zorana
Author: Stojkovska, Irena
Author: Kresoja, Milena
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.
Publisher: Global Science Press
Relation: Ministry of Education, Science and Technology Development of Serbia grant No. 174030 and Ss. Cyril and Methodius University of Skopje, Macedonia scientific research projects for 2014/2015 academic year
Identifier: oai:repository.ukim.mk:20.500.12188/6662
Identifier: http://hdl.handle.net/20.500.12188/6662Identifier: 10.4208/jcm.1710-m2017-0021
Identifier: https://www.global-sci.org/intro/article_detail/jcm/12650.htmlIdentifier: 37
Identifier: 1
