7,286 research outputs found
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
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
q-Gaussian based Smoothed Functional Algorithm for Stochastic Optimization
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.Comment: 5 pages, 1 figur
Online Sequential Monte Carlo smoother for partially observed stochastic differential equations
This paper introduces a new algorithm to approximate smoothed additive
functionals for partially observed stochastic differential equations. This
method relies on a recent procedure which allows to compute such approximations
online, i.e. as the observations are received, and with a computational
complexity growing linearly with the number of Monte Carlo samples. This online
smoother cannot be used directly in the case of partially observed stochastic
differential equations since the transition density of the latent data is
usually unknown. We prove that a similar algorithm may still be defined for
partially observed continuous processes by replacing this unknown quantity by
an unbiased estimator obtained for instance using general Poisson estimators.
We prove that this estimator is consistent and its performance are illustrated
using data from two models
Moment-Based Variational Inference for Markov Jump Processes
We propose moment-based variational inference as a flexible framework for
approximate smoothing of latent Markov jump processes. The main ingredient of
our approach is to partition the set of all transitions of the latent process
into classes. This allows to express the Kullback-Leibler divergence between
the approximate and the exact posterior process in terms of a set of moment
functions that arise naturally from the chosen partition. To illustrate
possible choices of the partition, we consider special classes of jump
processes that frequently occur in applications. We then extend the results to
parameter inference and demonstrate the method on several examples.Comment: Accepted by the 36th International Conference on Machine Learning
(ICML 2019
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