Related papers: A Variance Reduction Method for Parametrized Stoch…
In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…
In this paper we present an enhancement of the regression-based variance reduction approaches recently proposed in Belomestny et al. This enhancement is based on a truncation of the control variate and allows for a significant reduction of…
We present a numerical method for the frequent pricing of financial derivatives that depends on a large number of variables. The method is based on the construction of a polynomial basis to interpolate the value function of the problem by…
Solving chance-constrained stochastic optimal control problems is a significant challenge in control. This is because no analytical solutions exist for up to a handful of special cases. A common and computationally efficient approach for…
In this work, we propose viable and efficient strategies for stabilized parametrized advection dominated problems, with random inputs. In particular, we investigate the combination of wRB (weighted reduced basis) method for stochastic…
We consider the computation of averaged coefficients for the homogenization of elliptic partial differential equations. In this problem, like in many multiscale problems, a large number of similar computations parametrized by the…
We consider the Heston model as an example of a parameterized parabolic partial differential equation. A space-time variational formulation is derived that allows for parameters in the coefficients (for calibration) as well as choosing the…
Control variates are a well-established tool to reduce the variance of Monte Carlo estimators. However, for large-scale problems including high-dimensional and large-sample settings, their advantages can be outweighed by a substantial…
In many high-frequency simulation workflows, eigenvalue tracking along a parameter variation is necessary. This can become computationally prohibitive when repeated time-consuming eigenvalue problems must be solved. Therefore, we employ a…
Modern stochastic optimization methods often rely on uniform sampling which is agnostic to the underlying characteristics of the data. This might degrade the convergence by yielding estimates that suffer from a high variance. A possible…
Recently, we and several other authors have written about the possibilities of using stochastic approximation techniques for fitting variational approximations to intractable Bayesian posterior distributions. Naive implementations of…
The offline time of the reduced basis method can be very long given a large training set of parameter samples. This usually happens when the system has more than two independent parameters. On the other hand, if the training set includes…
In this paper, we propose an original approach to stochastic control problems. We consider a weak formulation that is written as an optimization (minimization) problem on the space of probability measures. We then introduce a penalized…
Reduced basis methods provide an efficient way of mapping out phase diagrams of strongly correlated many-body quantum systems. The method relies on using the exact solutions at select parameter values to construct a low-dimensional basis,…
This article describes an approach for parametrizing input and state trajectories in model predictive control. The parametrization is designed to be invariant to time shifts, which enables warm-starting the successive optimization problems…
Variational inference is increasingly being addressed with stochastic optimization. In this setting, the gradient's variance plays a crucial role in the optimization procedure, since high variance gradients lead to poor convergence. A…
The focus is on a model reduction framework for parameterized elliptic eigenvalue problems by a reduced basis method. In contrast to the standard single output case, one is interested in approximating several outputs simultaneously, namely…
The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…
This study proposes a method for designing stabilizing suboptimal controllers for nonlinear stochastic systems. These systems include time-invariant stochastic parameters that represent uncertainty of dynamics, posing two key difficulties…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…