Related papers: A Variance Reduction Method for Parametrized Stoch…
We address the application of stochastic optimization methods for the simultaneous control of parameter-dependent systems. In particular, we focus on the classical Stochastic Gradient Descent (SGD) approach of Robbins and Monro, and on the…
This paper presents a robust controller using a Linear Parameter Varying (LPV) model of the lane-keeping system with parameter reduction. Both varying vehicle speed and roll motion on a curved road influence the lateral vehicle model…
In this paper, we investigate diagonal estimation for large or implicit matrices, aiming to develop a novel and efficient stochastic algorithm that incorporates adaptive parameter selection. We explore the influence of different eigenvalue…
We propose a new stochastic optimization framework for empirical risk minimization problems such as those that arise in machine learning. The traditional approaches, such as (mini-batch) stochastic gradient descent (SGD), utilize an…
A number of optimization approaches have been proposed for optimizing nonconvex objectives (e.g. deep learning models), such as batch gradient descent, stochastic gradient descent and stochastic variance reduced gradient descent. Theory…
This paper considers stochastic-constrained stochastic optimization where the stochastic constraint is to satisfy that the expectation of a random function is below a certain threshold. In particular, we study the setting where data samples…
We consider optimal control of an elliptic two-point boundary value problem governed by functions of bounded variation (BV). The cost functional is composed of a tracking term for the state and the BV-seminorm of the control. We use the…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
A new approach for enhancing the process-variation tolerance of digital circuits is described. We extend recent advances in statistical timing analysis into an optimization framework. Our objective is to reduce the performance variance of a…
The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an It\^o type stochastic differential equation with control process entering both in the drift and the…
Off-policy learning is powerful for reinforcement learning. However, the high variance of off-policy evaluation is a critical challenge, which causes off-policy learning falls into an uncontrolled instability. In this paper, for reducing…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
In this paper, based on real-time nonlinear receding horizon control methodology, a novel approach is developed for parameter estimation of time invariant and time varying nonlinear dynamical systems in chaotic environments. Here, the…
This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing…
Large dimensional least-squares and regularised least-squares problems are expensive to solve. There exist many approximate techniques, some deterministic (like conjugate gradient), some stochastic (like stochastic gradient descent). Among…
Many problems involve the use of models which learn probability distributions or incorporate randomness in some way. In such problems, because computing the true expected gradient may be intractable, a gradient estimator is used to update…
The precision of lattice QCD calculations is often hindered by the stochastic noise inherent in these methods. The control variates method can provide an effective noise reduction but are typically constructed using heuristic approaches,…
We present a reduced basis (RB) method for parametrized linear elliptic partial differential equations (PDEs) in a least-squares finite element framework. A rigorous and reliable error estimate is developed, and is shown to bound the error…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
Locally adapted parameterizations of a model (such as locally weighted regression) are expressive but often suffer from high variance. We describe an approach for reducing the variance, based on the idea of estimating simultaneously a…