Policy Gradient Optimal Correlation Search for Variance Reduction in Monte Carlo simulation and Maximum Optimal Transport

• URL: http://arxiv.org/abs/2307.12703v2
• Date: Fri, 15 Sep 2023 15:43:25 GMT
• Title: Policy Gradient Optimal Correlation Search for Variance Reduction in Monte Carlo simulation and Maximum Optimal Transport
• Authors: Pierre Bras, Gilles Pag\`es
• Abstract summary: We propose a new algorithm for variance reduction when estimating $f(X_T)$ where $X$ is the solution to some differential equation and $f$ is a test function. The new estimator is $(f(XT) + f(X2_T))/2$, where $X1$ and $X2$ have same marginal law as $X2$ but are pathwise correlated so that to reduce the variance.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a new algorithm for variance reduction when estimating $f(X_T)$ where $X$ is the solution to some stochastic differential equation and $f$ is a test function. The new estimator is $(f(X^1_T) + f(X^2_T))/2$, where $X^1$ and $X^2$ have same marginal law as $X$ but are pathwise correlated so that to reduce the variance. The optimal correlation function $\rho$ is approximated by a deep neural network and is calibrated along the trajectories of $(X^1, X^2)$ by policy gradient and reinforcement learning techniques. Finding an optimal coupling given marginal laws has links with maximum optimal transport.

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