Machine learning driven extended matrix norm method for the solution of large-scale zero-sum matrix games

Abstract

In this paper, we develop a novel machine learning-driven framework for solving large-scale zero-sum matrix games by exploiting patterns discovered from the offline extended matrix norm method. Modern game theoretic tools such as the extended matrix norm method allow rapid estimation of the game values for small-scale zero-sum games by computing norms of the payoff matrix. However, as the number of strategies in the game increases, obtaining an accurate value estimation through the extended matrix norm method becomes more difficult. In this work, we propose a novel neural network architecture for large-scale zero-sum matrix games, which takes the estimations of the extended matrix norm method and payoff matrix as inputs, and provides a rapid estimation of the game value as the output. The proposed architecture is trained over various random zero-sum games of different dimensions. Results show that the developed framework can obtain accurate value predictions, with a less than 10% absolute relative error, for games with up to 50 strategies. Also of note, after the network is trained, solution predictions can be obtained in real-time, which makes the proposed method particularly useful for real-world applications.