A unified view of likelihood ratio and reparameterization gradients

by   Paavo Parmas, et al.

Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used to estimate gradients of expectations throughout machine learning and reinforcement learning; however, they are usually explained as simple mathematical tricks, with no insight into their nature. We use a first principles approach to explain that LR and RP are alternative methods of keeping track of the movement of probability mass, and the two are connected via the divergence theorem. Moreover, we show that the space of all possible estimators combining LR and RP can be completely parameterized by a flow field u(x) and an importance sampling distribution q(x). We prove that there cannot exist a single-sample estimator of this type outside our characterized space, thus, clarifying where we should be searching for better Monte Carlo gradient estimators.


page 1

page 2

page 3

page 4


A unified view of likelihood ratio and reparameterization gradients and an optimal importance sampling scheme

Reparameterization (RP) and likelihood ratio (LR) gradient estimators ar...

Variational inference for Monte Carlo objectives

Recent progress in deep latent variable models has largely been driven b...

Monte Carlo Gradient Estimation in Machine Learning

This paper is a broad and accessible survey of the methods we have at ou...

New Tricks for Estimating Gradients of Expectations

We derive a family of Monte Carlo estimators for gradients of expectatio...

Renewal Monte Carlo: Renewal theory based reinforcement learning

In this paper, we present an online reinforcement learning algorithm, ca...

DiCE: The Infinitely Differentiable Monte-Carlo Estimator

The score function estimator is widely used for estimating gradients of ...

Please sign up or login with your details

Forgot password? Click here to reset