Valuation problems, such as attribution-based feature interpretation, data valuation and model valuation for ensembles, become increasingly more important in many machine learning applications. Such problems are commonly solved by well-known game-theoretic criteria, such as Shapley value or Banzhaf index. In this work, we present a novel energy-based treatment for cooperative games, with a theoretical justification by the maximum entropy framework. Surprisingly, by conducting variational inference of the energy-based model, we recover various game-theoretic valuation criteria, such as Shapley value and Banzhaf index, through conducting one-step gradient ascent for maximizing the mean-field ELBO objective. This observation also verifies the rationality of existing criteria, as they are all trying to decouple the correlations among the players through the mean-field approach. By running gradient ascent for multiple steps, we achieve a trajectory of the valuations, among which we define the valuation with the best conceivable decoupling error as the Variational Index. We experimentally demonstrate that the proposed Variational Index enjoys intriguing properties on certain synthetic and real-world valuation problems.

提出了一种基于能量的处理合作博弈问题的方法，通过变分推断模型进行一步固定点迭代，恢复出各种博弈论估价标准，并证明这些变分估价都满足一组博弈论公理，并在某些合成和实际的评估问题上实验表明所提出的变分索引具有更低的解耦误差和更好的估值性能。

协作游戏的能量学习，及其在机器学习估值问题中的应用