Related papers: A Variance Reduction Method for Parametrized Stoch…
Domain randomization is a simple, effective, and flexible scheme for obtaining robust feedback policies aimed at reducing the sim-to-real gap due to model mismatch. While domain randomization methods have yielded impressive demonstrations…
This paper provides a unifying theoretical framework for stochastic optimization algorithms by means of a latent stochastic variational problem. Using techniques from stochastic control, the solution to the variational problem is shown to…
We consider the estimation of parameter-dependent statistics of functional outputs of elliptic boundary value problems (BVPs) with parametrized random and deterministic inputs. For a given value of the deterministic paremeter, a stochastic…
In this paper we investigate infinite horizon optimal control problems for parametrized partial differential equations. We are interested in feedback control via dynamic programming equations which is well-known to suffer from the curse of…
Monte Carlo estimation in plays a crucial role in stochastic reaction networks. However, reducing the statistical uncertainty of the corresponding estimators requires sampling a large number of trajectories. We propose control variates…
This paper presents a control variate-based Markov chain Monte Carlo algorithm for efficient sampling from the probability simplex, with a focus on applications in large-scale Bayesian models such as latent Dirichlet allocation. Standard…
A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the…
The central objective of this paper is to develop reduced basis methods for parameter dependent transport dominated problems that are rigorously proven to exhibit rate-optimal performance when compared with the Kolmogorov $n$-widths of the…
We present an efficient finite difference method for the approximation of second derivatives, with respect to system parameters, of expectations for a class of discrete stochastic chemical reaction networks. The method uses a coupling of…
We present a parameter estimation method in Ordinary Differential Equation (ODE) models. Due to complex relationships between parameters and states the use of standard techniques such as nonlinear least squares can lead to the presence of…
Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…
We consider a composite convex minimization problem associated with regularized empirical risk minimization, which often arises in machine learning. We propose two new stochastic gradient methods that are based on stochastic dual averaging…
We consider parametrized linear-quadratic optimal control problems and provide their online-efficient solutions by combining greedy reduced basis methods and machine learning algorithms. To this end, we first extend the greedy control…
The development of efficient numerical methods for kinetic equations with stochastic parameters is a challenge due to the high dimensionality of the problem. Recently we introduced a multiscale control variate strategy which is capable to…
We present a class of reduced basis (RB) methods for the iterative solution of parametrized symmetric positive-definite (SPD) linear systems. The essential ingredients are a Galerkin projection of the underlying parametrized system onto a…
Parameter fitting of data to a proposed equation almost always consider these parameters as independent variables. Here, the method proposed optimizes an arbitrary number of variables by the minimization of a function of a single variable.…
The most common approaches for solving multistage stochastic programming problems in the research literature have been to either use value functions ("dynamic programming") or scenario trees ("stochastic programming") to approximate the…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
This work is on a user-friendly reduced basis method for solving a family of parametric PDEs by preconditioned Krylov subspace methods including the conjugate gradient method, generalized minimum residual method, and bi-conjugate gradient…
Bayesian inference for inverse problems involves computing expectations under posterior distributions -- e.g., posterior means, variances, or predictive quantities -- typically via Monte Carlo (MC) estimation. When the quantity of interest…