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A Strong Law of Large Numbers for Random Monotone Operators
Random monotone operators are stochastic versions of maximal monotone operators which play an important role in stochastic nonsmooth optimization....
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Convergence of Gradient Algorithms for Nonconvex C1+α Cost Functions
This paper is concerned with convergence of stochastic gradient algorithms with momentum terms in the nonconvex setting. A class of stochastic...
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Convergence analysis of Oja’s iteration for solving online PCA with nonzero-mean samples
Principal component analysis (PCA) is one of the most popular multivariate data analysis techniques for dimension reduction and data mining, and is...
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Fast and strong convergence of online learning algorithms
In this paper, we study the online learning algorithm without explicit regularization terms. This algorithm is essentially a stochastic gradient...
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Bayesian doubly adaptive randomization in clinical trials
Bayesian adaptive randomization has attracted increasingly attention in the literature and has been implemented in many phase II clinical trials....
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Online regularized learning with pairwise loss functions
Recently, there has been considerable work on analyzing learning algorithms with pairwise loss functions in the batch setting. There is relatively...
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Covariate-adaptive designs with missing covariates in clinical trials
Many covariate-adaptive randomization procedures have been proposed and implemented to balance important covariates in clinical trials. These methods...
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An adaptive design to assess the reliability of the pyrotechnic control subsystem in opening the solar array
The pyrotechnic control subsystem plays an important role in opening the solar array of a satellite. Assessing the reliability of the subsystem...
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Measures in the space of planes and convex bodies
The present paper gives two representations (so-called flag representations) for the measure of planes intersecting a convex body. These...
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Validation analysis of mirror descent stochastic approximation method
The main goal of this paper is to develop accuracy estimates for stochastic programming problems by employing stochastic approximation (SA) type...
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An optimal method for stochastic composite optimization
This paper considers an important class of convex programming (CP) problems, namely, the stochastic composite optimization (SCO), whose objective...
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The approximate solution of a nonlinear diffusion equation using some techniques, a comparison study
In this paper, the diffusion equation under square nonlinearity is solved using the WHEP technique, the Homotopy perturbation method (HPM) and...
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A stochastic gradient type algorithm for closed-loop problems
We focus on the numerical solution of closed-loop stochastic problems, and propose a perturbed gradient algorithm to achieve this goal. The main...
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Recursive parameter estimation: convergence
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple...
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How does a stochastic optimization/approximation algorithm adapt to a randomly evolving optimum/root with jump Markov sample paths
Stochastic optimization/approximation algorithms are widely used to recursively estimate the optimum of a suitable function or its root under noisy...
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Online Gradient Descent Learning Algorithms
This paper considers the least-square online gradient descent algorithm in a reproducing kernel Hilbert space (RKHS) without an explicit...
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Global Optimization Using Diffusion Perturbations with Large Noise Intensity
This work develops an algorithm for global optimization. The algorithm is of gradient ascent type and uses random perturbations. In contrast to the...
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Online Learning Algorithms
In this paper, we study an online learning algorithm in Reproducing Kernel Hilbert Spaces (RKHSs) and general Hilbert spaces. We present a general...
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Estimation of an optimal solution of a LP problem with unknown objective function
We consider a linear programming problem with unknown objective function. Random observations related to the unknown objective function are...
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On a Class of Stochastic Integral Operators of McShane Type
The aim of this note is to give an extension of a result by McShane to a general stochastic integral operator with a non-Lipschitz condition on the...