Training neural control variates using correlated configurations

TL;DR

This paper investigates how using autocorrelated samples from MCMC can improve the training of neural control variates, leading to better variance reduction in Monte Carlo simulations, especially with limited data.

Contribution

It systematically analyzes the impact of correlated configurations on NCV training and demonstrates their benefits through theoretical insights and numerical experiments.

Findings

Correlated samples can enhance NCV performance.

Training on autocorrelated data is beneficial with limited resources.

Empirical results show improved variance reduction in gauge and scalar field theories.

Abstract

Neural control variates (NCVs) have emerged as a powerful tool for variance reduction in Monte Carlo (MC) simulations, particularly in high-dimensional problems where traditional control variates are difficult to construct analytically. By training neural networks to learn auxiliary functions correlated with the target observable, NCVs can significantly reduce estimator variance while preserving unbiasedness. However, a critical but often overlooked aspect of NCV training is the role of autocorrelated samples generated by Markov Chain Monte Carlo (MCMC). While such samples are typically discarded for error estimation due to their statistical redundancy, they may contain useful information about the structure of the underlying probability distribution that can benefit the training process. In this work, we systematically examine the effect of using correlated configurations in training neural control variates. We demonstrate, both conceptually and numerically, that training on correlated data can improve control variate performance, especially in settings with limited computational resources. Our analysis includes empirical results from $U(1)$ gauge theory and scalar field theory, illustrating when and how autocorrelated samples enhance NCV construction. These findings provide practical guidance for the efficient use of MCMC data in training neural networks.