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

arXiv: https://arxiv.org/abs/2307.12703 · HTML: https://mlsanity.com/paper/2307.12703/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 24 Jul 2023.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Deep Learning Approximation for Stochastic Control Problems](https://mlsanity.com/paper/1611.07422/) (2016)
- [Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: II -- The Finite Horizon Case](https://mlsanity.com/paper/1908.01613/) (2019)
- [Deep neural networks algorithms for stochastic control problems on finite horizon: convergence analysis](https://mlsanity.com/paper/1812.04300/) (2018)
- [Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications](https://mlsanity.com/paper/1812.05916/) (2018)
- [Deep Forward-Backward SDEs for Min-max Control](https://mlsanity.com/paper/1906.04771/) (2019)
- [Performance of a Markovian neural network versus dynamic programming on a fishing control problem](https://mlsanity.com/paper/2109.06856/) (2021)

## Built on by (most cited first, 1 of 1)

- [Reinforcement Learning for Adaptive MCMC](https://mlsanity.com/paper/2405.13574/) (2024)

## Abstract (arXiv)

We propose a new algorithm for variance reduction when estimating f(XT) where X is the solution to some stochastic differential equation and f is a test function. The new estimator is (f(X1T) + f(X2T))/2, where X1 and X2 have same marginal law as X but are pathwise correlated so that to reduce the variance. The optimal correlation function ρ is approximated by a deep neural network and is calibrated along the trajectories of (X1, X2) by policy gradient and reinforcement learning techniques. Finding an optimal coupling given marginal laws has links with maximum optimal transport.