Newton based Stochastic Optimization using q-Gaussian Smoothed Functional Algorithms

We present the first q-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 q-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 et al., 2013), we presented gradient SF algorithms based on the q-Gaussian perturbations. Our work extends prior work on smoothed functional algorithms by generalizing the class of perturbation distributions as most distributions reported in the literature for which SF algorithms are known to work and turn out to be special cases of the q-Gaussian distribution. Besides studying the convergence properties of our algorithm analytically, we also show the results of several 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 q-values, in comparison to Newton SF algorithms with the Gaussian (Bhatnagar, 2007) and Cauchy perturbations, as well as the gradient q-Gaussian SF algorithms (Ghoshdastidar et al., 2013).Comment: This is a longer of version of the paper with the same title accepted in Automatic

Smoothed Functional Algorithms for Stochastic Optimization using q-Gaussian Distributions

Smoothed functional (SF) schemes for gradient estimation are known to be efficient in stochastic optimization algorithms, specially 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 literature, which include Gaussian, Cauchy and uniform distributions among others. This paper studies a new class of kernels based on the q-Gaussian distribution, that 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 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

Local-Aggregate Modeling for Big-Data via Distributed Optimization: Applications to Neuroimaging

Technological advances have led to a proliferation of structured big data that have matrix-valued covariates. We are specifically motivated to build predictive models for multi-subject neuroimaging data based on each subject's brain imaging scans. This is an ultra-high-dimensional problem that consists of a matrix of covariates (brain locations by time points) for each subject; few methods currently exist to fit supervised models directly to this tensor data. We propose a novel modeling and algorithmic strategy to apply generalized linear models (GLMs) to this massive tensor data in which one set of variables is associated with locations. Our method begins by fitting GLMs to each location separately, and then builds an ensemble by blending information across locations through regularization with what we term an aggregating penalty. Our so called, Local-Aggregate Model, can be fit in a completely distributed manner over the locations using an Alternating Direction Method of Multipliers (ADMM) strategy, and thus greatly reduces the computational burden. Furthermore, we propose to select the appropriate model through a novel sequence of faster algorithmic solutions that is similar to regularization paths. We will demonstrate both the computational and predictive modeling advantages of our methods via simulations and an EEG classification problem.Comment: 41 pages, 5 figures and 3 table

Blind deconvolution of medical ultrasound images: parametric inverse filtering approach

©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TIP.2007.910179The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging. In this paper, this problem is addressed via proposing a blind deconvolution method which is innovative in several ways. In particular, the method is based on parametric inverse filtering, whose parameters are optimized using two-stage processing. At the first stage, some partial information on the point spread function is recovered. Subsequently, this information is used to explicitly constrain the spectral shape of the inverse filter. From this perspective, the proposed methodology can be viewed as a ldquohybridizationrdquo of two standard strategies in blind deconvolution, which are based on either concurrent or successive estimation of the point spread function and the image of interest. Moreover, evidence is provided that the ldquohybridrdquo approach can outperform the standard ones in a number of important practical cases. Additionally, the present study introduces a different approach to parameterizing the inverse filter. Specifically, we propose to model the inverse transfer function as a member of a principal shift-invariant subspace. It is shown that such a parameterization results in considerably more stable reconstructions as compared to standard parameterization methods. Finally, it is shown how the inverse filters designed in this way can be used to deconvolve the images in a nonblind manner so as to further improve their quality. The usefulness and practicability of all the introduced innovations are proven in a series of both in silico and in vivo experiments. Finally, it is shown that the proposed deconvolution algorithms are capable of improving the resolution of ultrasound images by factors of 2.24 or 6.52 (as judged by the autocorrelation criterion) depending on the type of regularization method used

Simultaneous Perturbation Algorithms for Batch Off-Policy Search

We propose novel policy search algorithms in the context of off-policy, batch mode reinforcement learning (RL) with continuous state and action spaces. Given a batch collection of trajectories, we perform off-line policy evaluation using an algorithm similar to that by [Fonteneau et al., 2010]. Using this Monte-Carlo like policy evaluator, we perform policy search in a class of parameterized policies. We propose both first order policy gradient and second order policy Newton algorithms. All our algorithms incorporate simultaneous perturbation estimates for the gradient as well as the Hessian of the cost-to-go vector, since the latter is unknown and only biased estimates are available. We demonstrate their practicality on a simple 1-dimensional continuous state space problem