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The Shapley value, which is arguably the most popular approach for assigninga meaningful contribution value to players in a cooperative game, has recentlybeen used intensively in explainable artificial intelligence. Itsmeaningfulness is due to axiomatic properties that only the Shapley valuesatisfies, which, however, comes at the expense of an exact computation growingexponentially with the number of agents. Accordingly, a number of works aredevoted to the efficient approximation of the Shapley value, most of themrevolve around the notion of an agent's marginal contribution. In this paper,we propose with SVARM and Stratified SVARM two parameter-free anddomain-independent approximation algorithms based on a representation of theShapley value detached from the notion of marginal contribution. We proveunmatched theoretical guarantees regarding their approximation quality andprovide empirical results including synthetic games as well as commonexplainability use cases comparing ourselves with state-of-the-art methods.

Approximating the Shapley Value without Marginal Contributions