2020/02/14 by Gauthier Gidel, David Balduzzi, Gidel, Gauthier +7
Computer Science · #Adversarial Robustness in Machine Learning #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Reinforcement Learning in Robotics #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2002.05820
openalex publication_date 2020/02/14 · openalex created_date 2021/03/29 · openalex updated_date 2026/07/28
Adversarial training, a special case of multi-objective optimization, is an increasingly prevalent machine learning technique: some of its most notable applications include GAN-based generative modeling and self-play techniques in reinforcement learning which have been applied to complex games such as Go or Poker. In practice, a single pair of networks is typically trained in order to find an approximate equilibrium of a highly nonconcave-nonconvex adversarial problem. However, while a classic result in game theory states such an equilibrium exists in concave-convex games, there is no analogous guarantee if the payoff is nonconcave-nonconvex. Our main contribution is to provide an approximate minimax theorem for a large class of games where the players pick neural networks including WGAN, StarCraft II, and Blotto Game. Our findings rely on the fact that despite being nonconcave-nonconvex with respect to the neural networks parameters, these games are concave-convex with respect to the actual models (e.g., functions or distributions) represented by these neural networks.