Shapley Value Approximation Based on Complementary Contribution

Abstract

Shapley value provides a unique way to fairly assess each player's contribution in a coalition and has enjoyed many applications. However, the exact computation of Shapley value is #P-hard due to the combinatoric nature of Shapley value. Many existing applications of Shapley value are based on Monte-Carlo approximation, which requires a large number of samples and the assessment of utility on many coalitions to reach high-quality approximation, and thus is still far from being efficient. Can we achieve an efficient approximation of Shapley value by smartly obtaining samples? In this paper, we treat the sampling approach to Shapley value approximation as a stratified sampling problem. Our main technical contributions are a novel stratification design and a sampling method based on Neyman allocation. Moreover, computing the Shapley value in a dynamic setting, where new players may join the game and others may leave it poses an additional challenge due to the considerable cost of recomputing from scratch. To tackle this issue, we propose to capture changes in Shapley value, making our approaches applicable to scenarios with dynamic players. Experimental results on several real data sets and synthetic data sets demonstrate the effectiveness and efficiency of our approaches.