2019/05/15 by Arvind U. Raghunathan, Raghunathan, Arvind U., Anoop Cherian +3 · 4 citations
Decision Sciences · Physics and Astronomy · #Advanced Bandit Algorithms Research #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Applications #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Opinion Dynamics and Social Influence #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1905.05927
openalex publication_date 2019/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Computing Nash equilibrium (NE) of multi-player games has witnessed renewed interest due to recent advances in generative adversarial networks. However, computing equilibrium efficiently is challenging. To this end, we introduce the Gradient-based Nikaido-Isoda (GNI) function which serves: (i) as a merit function, vanishing only at the first-order stationary points of each player's optimization problem, and (ii) provides error bounds to a stationary Nash point. Gradient descent is shown to converge sublinearly to a first-order stationary point of the GNI function. For the particular case of bilinear min-max games and multi-player quadratic games, the GNI function is convex. Hence, the application of gradient descent in this case yields linear convergence to an NE (when one exists). In our numerical experiments, we observe that the GNI formulation always converges to the first-order stationary point of each player's optimization problem.