A Review of the Gumbel-max Trick and its Extensions for Discrete Stochasticity in Machine Learning

TL;DR

This survey reviews the Gumbel-max trick and its extensions, highlighting their applications in machine learning for sampling, structured domains, and gradient estimation, and discusses future research directions.

Contribution

It provides a comprehensive overview of Gumbel-max trick extensions, their applications, and design choices, aiding algorithm selection in machine learning.

Findings

Extensive overview of Gumbel-max trick and its extensions.

Summary of applications in machine learning including sampling and gradient estimation.

Discussion of design choices and future research directions.

Abstract

The Gumbel-max trick is a method to draw a sample from a categorical distribution, given by its unnormalized (log-)probabilities. Over the past years, the machine learning community has proposed several extensions of this trick to facilitate, e.g., drawing multiple samples, sampling from structured domains, or gradient estimation for error backpropagation in neural network optimization. The goal of this survey article is to present background about the Gumbel-max trick, and to provide a structured overview of its extensions to ease algorithm selection. Moreover, it presents a comprehensive outline of (machine learning) literature in which Gumbel-based algorithms have been leveraged, reviews commonly-made design choices, and sketches a future perspective.