Newton-based stochastic optimization using qq-Gaussian smoothed functional algorithms

We present the first qq-Gaussian smoothed functional (SF) estimator of the Hessian and the first Newton-based stochastic optimization algorithm that estimates both the Hessian and the gradient of the objective function using qq-Gaussian perturbations. Our algorithm requires only two system simulations (regardless of the parameter dimension) and estimates both the gradient and the Hessian at each update epoch using these. We also present a proof of convergence of the proposed algorithm. In a related recent work (Ghoshdastidar, Dukkipati, & Bhatnagar, 2014), we presented gradient SF algorithms based on the qq-Gaussian perturbations. Our work extends prior work on SF algorithms by generalizing the class of perturbation distributions as most distributions reported in the literature for which SF algorithms are known to work turn out to be special cases of the qq-Gaussian distribution. Besides studying the convergence properties of our algorithm analytically, we also show the results of numerical simulations on a model of a queuing network, that illustrate the significance of the proposed method. In particular, we observe that our algorithm performs better in most cases, over a wide range of qq-values, in comparison to Newton SF algorithms with the Gaussian and Cauchy perturbations, as well as the gradient qq-Gaussian SF algorithms.