Monte Carlo Gradient Estimation in Machine Learning

TL;DR

This paper provides a comprehensive survey of Monte Carlo gradient estimation methods in machine learning, discussing their development, assumptions, and applications across various learning paradigms to facilitate further research and improvements.

Contribution

It offers an accessible overview of three key Monte Carlo gradient estimators, their historical context, relationships, and potential for generalization, supporting future advances in the field.

Findings

Exploration of pathwise, score function, and measure-valued estimators

Analysis of their historical development and assumptions

Discussion on combining and generalizing these methods

Abstract

This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a function with respect to parameters defining the distribution that is integrated; the problem of sensitivity analysis. In machine learning research, this gradient problem lies at the core of many learning problems, in supervised, unsupervised and reinforcement learning. We will generally seek to rewrite such gradients in a form that allows for Monte Carlo estimation, allowing them to be easily and efficiently used and analysed. We explore three strategies--the pathwise, score function, and measure-valued gradient estimators--exploring their historical development, derivation, and underlying assumptions. We describe their use in other fields, show how they are related and can be combined, and expand on their possible generalisations. Wherever Monte Carlo gradient estimators have been derived and deployed in the past, important advances have followed. A deeper and more widely-held understanding of this problem will lead to further advances, and it is these advances that we wish to support.