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The Gumbel-max trick is a method to draw a sample from a categoricaldistribution, given by its unnormalized (log-)probabilities. Over the pastyears, the machine learning community has proposed several extensions of thistrick to facilitate, e.g., drawing multiple samples, sampling from structureddomains, or gradient estimation for error backpropagation in neural networkoptimization. The goal of this survey article is to present background aboutthe Gumbel-max trick, and to provide a structured overview of its extensions toease algorithm selection. Moreover, it presents a comprehensive outline of(machine learning) literature in which Gumbel-based algorithms have beenleveraged, reviews commonly-made design choices, and sketches a futureperspective.

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