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.
Arvind Raghunathan (Mitsubishi Electric Research Laboratories)
Anoop Cherian (MERL)
Devesh Jha (Mitsubishi Electric Research Labs)
Related Events (a corresponding poster, oral, or spotlight)
2019 Oral: Game Theoretic Optimization via Gradient-based Nikaido-Isoda Function »
Tue Jun 11th 11:20 -- 11:25 AM Room Room 102