Finding and Only Finding Differential Nash Equilibria by Both Pretending to be a Follower

Xuchan Bao, Guodong Zhang

Abstract: Finding Nash equilibria in two-player differentiable games is a classical problem in game theory with important relevance in machine learning. We propose double Follow-the-Ridge (double-FTR), an algorithm that locally converges to and only to differential Nash equilibria in general-sum two-player differentiable games. To our knowledge, double-FTR is the first algorithm with such guarantees for general-sum games. Furthermore, we show that by varying its preconditioner, double-FTR leads to a broader family of algorithms with the same convergence guarantee. In addition, double-FTR avoids oscillation near equilibria due to the real-eigenvalues of its Jacobian at fixed points. Empirically, we validate the double-FTR algorithm on a range of simple zero-sum and general sum games, as well as simple Generative Adversarial Network (GAN) tasks.

Certifications: Featured Certification

Submission Length: Regular submission (no more than 12 pages of main content)

Code: https://github.com/XuchanBao/double-ftr

Assigned Action Editor: ~Michael_Bowling1

License: Creative Commons Attribution 4.0 International (CC BY 4.0)

Submission Number: 953