Smoothed Functional Algorithms for Stochastic Optimization Using q-Gaussian Distributions

Ghoshdastidar, Debarghya and Dukkipati, Ambedkar and Bhatnagar, Shalabh (2014) Smoothed Functional Algorithms for Stochastic Optimization Using q-Gaussian Distributions. In: ACM TRANSACTIONS ON MODELING AND COMPUTER SIMULATION, 24 (3).

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Abstract

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 demonstrate their performance numerically through simulations on a queuing model.

Item Type:	Journal Article
Publication:	ACM TRANSACTIONS ON MODELING AND COMPUTER SIMULATION
Additional Information:	Copy right for this article belongs to the ASSOC COMPUTING MACHINERY, 2 PENN PLAZA, STE 701, NEW YORK, NY 10121-0701 USA
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	10 Oct 2014 09:14
Last Modified:	10 Oct 2014 09:14
URI:	http://eprints.iisc.ac.in/id/eprint/49989

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