q-Gaussian based Smoothed Functional Algorithm for Stochastic Optimization

TL;DR

This paper introduces a novel stochastic optimization algorithm using q-Gaussian based smoothed functional gradient estimation, demonstrating convergence and improved performance through simulations on a queuing model.

Contribution

It proposes a new q-Gaussian based smoothed functional method for stochastic optimization, including convergence analysis and practical simulation results.

Findings

Convergence of the proposed algorithm is established.

Simulation results show improved optimization performance.

The method effectively handles power-law behaviors in data.

Abstract

The q-Gaussian distribution results from maximizing certain generalizations of Shannon entropy under some constraints. The importance of q-Gaussian distributions stems from the fact that they exhibit power-law behavior, and also generalize Gaussian distributions. In this paper, we propose a Smoothed Functional (SF) scheme for gradient estimation using q-Gaussian distribution, and also propose an algorithm for optimization based on the above scheme. Convergence results of the algorithm are presented. Performance of the proposed algorithm is shown by simulation results on a queuing model.