Smoothed functional algorithms for stochastic optimization using q-gaussian distributions

Debarghya Ghoshdastidar, Ambedkar Dukkipati, Shalabh Bhatnagar

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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.

Original languageEnglish
Article number17
JournalACM Transactions on Modeling and Computer Simulation
Volume24
Issue number3
DOIs
StatePublished - May 2014
Externally publishedYes

Keywords

  • Projected gradient based search
  • Q-Gaussian
  • Smoothed functional algorithms
  • Two-timescale stochastic approximation

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