A Review of the Gumbel-max Trick and its Extensions for Discrete Stochasticity in Machine Learning
It synthesizes existing knowledge for researchers and practitioners working with discrete variables in ML, but is incremental as it does not introduce new methods.
This survey article reviews the Gumbel-max trick and its extensions for handling discrete stochasticity in machine learning, providing a structured overview to aid algorithm selection and outlining applications and future directions.
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.