Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Smoothed Functional Algorithms for Stochastic Optimization Using q -Gaussian Distributions

Smoothed Functional Algorithms for Stochastic Optimization Using q -Gaussian Distributions Smoothed Functional Algorithms for Stochastic Optimization Using q -Gaussian Distributions DEBARGHYA GHOSHDASTIDAR, AMBEDKAR DUKKIPATI, and SHALABH BHATNAGAR, Indian Institute of Science Smoothed functional (SF) schemes for gradient estimation are known to be efficient in stochastic optimization algorithms, especially when the objective is to improve the performance of a stochastic system. However, the performance of these methods depends on several parameters, such as the choice of a suitable smoothing kernel. Different kernels have been studied in the literature, which include Gaussian, Cauchy, and uniform distributions, among others. This article studies a new class of kernels based on the q-Gaussian distribution, which has gained popularity in statistical physics over the last decade. Though the importance of this family of distributions is attributed to its ability to generalize the Gaussian distribution, we observe that this class encompasses almost all existing smoothing kernels. This motivates us to study SF schemes for gradient estimation using the q-Gaussian distribution. Using the derived gradient estimates, we propose two-timescale algorithms for optimization of a stochastic objective function in a constrained setting with a projected gradient search approach. We prove the convergence of our algorithms to the set of stationary points of an associated ODE. We also http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Modeling and Computer Simulation (TOMACS) Association for Computing Machinery

Smoothed Functional Algorithms for Stochastic Optimization Using q -Gaussian Distributions

Download PDF
26 pages

Loading next page...
 
/lp/association-for-computing-machinery/smoothed-functional-algorithms-for-stochastic-optimization-using-q-R8jVKawwT5
Publisher
Association for Computing Machinery
Copyright
Copyright © 2014 by ACM Inc.
ISSN
1049-3301
DOI
10.1145/2628434
Publisher site
See Article on Publisher Site

Abstract

Smoothed Functional Algorithms for Stochastic Optimization Using q -Gaussian Distributions DEBARGHYA GHOSHDASTIDAR, AMBEDKAR DUKKIPATI, and SHALABH BHATNAGAR, Indian Institute of Science Smoothed functional (SF) schemes for gradient estimation are known to be efficient in stochastic optimization algorithms, especially when the objective is to improve the performance of a stochastic system. However, the performance of these methods depends on several parameters, such as the choice of a suitable smoothing kernel. Different kernels have been studied in the literature, which include Gaussian, Cauchy, and uniform distributions, among others. This article studies a new class of kernels based on the q-Gaussian distribution, which has gained popularity in statistical physics over the last decade. Though the importance of this family of distributions is attributed to its ability to generalize the Gaussian distribution, we observe that this class encompasses almost all existing smoothing kernels. This motivates us to study SF schemes for gradient estimation using the q-Gaussian distribution. Using the derived gradient estimates, we propose two-timescale algorithms for optimization of a stochastic objective function in a constrained setting with a projected gradient search approach. We prove the convergence of our algorithms to the set of stationary points of an associated ODE. We also

Journal

ACM Transactions on Modeling and Computer Simulation (TOMACS) – Association for Computing Machinery

Published: May 2, 2014

There are no references for this article.