MG-CNN: A deep CNN to predict saddle points of matrix games

Abstract

Finding the saddle point of a matrix game is a classical problem that arises in various fields, e.g., economics, computer science, and engineering. The standard problem-solving methods consist of formulating the problem as a linear program (LP). However, this approach seems less efficient when many instances need to be solved. In this paper, we propose a Convolutional Neural Network based approach, which is able to predict both the strategy profile (x,y) and the optimal value v of the game. We call this approach Matrix Game-Conventional Neural Network or MG-CNN for short. Thanks to a global pooling technique, MG-CNN can solve matrix games with different shapes. We propose a specialized algorithm to train MG-CNN, which includes both data generation and model training. Our numerical experiments show that MG-CNN outperforms standard LP solvers in terms of computational CPU time and provides a high-quality prediction.