In this work, we develop a reduced-basis approach for the e cient computation of parametrized expected values, for a large number of parameter values, using the control variate method to reduce the variance. Two algorithms are proposed to compute online, through a cheap reduced-basis approximation, the control variates for the computation of a large number of expectations of a functional of a p...

In multiple importance sampling we combine samples from a finite list of proposal distributions. When those proposal distributions are used to create control variates, it is possible (Owen and Zhou, 2000) to bound the ratio of the resulting variance to that of the unknown best proposal distribution in our list. The minimax regret arises by taking a uniform mixture of proposals, but that is cons...

Multi-model Monte Carlo methods, such as multi-level (MLMC) and multifidelity (MFMC), allow for efficient estimation of the expectation a quantity interest given set models varying fidelities. Recently, it was shown that MLMC MFMC estimators are both instances approximate control variates (ACV) framework [Gorodetsky et al. (2020) [14]]. In same work, also hand-tailored ACV could outperform vari...

Sufficient dimension reduction methods provide effective ways to visualize discriminant analysis problems. For example, Cook and Yin (2001) showed that the dimension reduction method of sliced average variance estimation (save) identifies variates that are equivalent to a quadratic discriminant analysis (qda) solution. This article makes this connection explicit to motivate the use of save vari...

In this paper we present a new approach to control variates for improving computational efficiency of Ensemble Monte Carlo. We present the approach using simulation of paths of a time-dependent nonlinear stochastic equation. The core idea is to extract information at one or more nominal model parameters and use this information to gain estimation efficiency at neighboring parameters. This idea ...

We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of control variates from classical Monte Carlo integration. We illustrate it using two models of nonequilibrium transport.

We develop a numerical method for pricing multidimensional vanilla options in the Black-Scholes framework. In low dimensions, we improve an adaptive integration algorithm proposed by two of the authors by introducing a new splitting strategy based on a geometrical criterion. In higher dimensions, this new algorithm is used as a control variate after a dimension reduction based on principal comp...

We propose an approach to a two-fold optimal parameter search for a combined variance reduction technique of the control variates and the important sampling in a suitable pure-jump Lévy process framework. The parameter search procedure is based on the two-time-scale stochastic approximation algorithm with equilibrated control variates component and with quasi-static importance sampling one. We ...

Policy optimization on high-dimensional action spaces exhibits its difficulty caused by the high variance of the policy gradient estimators. We present the action subspace dependent gradient (ASDG) estimator which incorporates the RaoBlackwell theorem (RB) and Control Variates (CV) into a unified framework to reduce the variance. To invoke RB, the algorithm learns the underlying factorization s...