Title: Neural Control Variates for Variance Reduction,
Abstract: In statistics and machine learning, approximation of an intractable
integration is often achieved by using the unbiased Monte Carlo estimator, but
the variances of the estimation are generally high in many applications.
Control variates approaches are well-known to reduce the variance of the
estimation. These control variates are typically constructed by employing
predefined parametric functions or polynomials, determined by using those
samples drawn from the relevant distributions. Instead, we propose to construct
those control variates by learning neural networks to handle the cases when
test functions are complex. In many applications, obtaining a large number of
samples for Monte Carlo estimation is expensive, which may result in
overfitting when training a neural network. We thus further propose to employ
auxiliary random variables induced by the original ones to extend data samples
for training the neural networks. We apply the proposed control variates with
augmented variables to thermodynamic integration and reinforcement learning.
Experimental results demonstrate that our method can achieve significant
variance reduction compared with other alternatives.