  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.
