Exponential Convergence of Gradient Methods in Concave Network Zero-sum Games

• URL: http://arxiv.org/abs/2007.05477v1
• Date: Fri, 10 Jul 2020 16:56:56 GMT
• Title: Exponential Convergence of Gradient Methods in Concave Network Zero-sum Games
• Authors: Amit Kadan and Hu Fu
• Abstract summary: We study the computation of Nash equilibrium in concave network zero-sum games (NZSGs) We show that various game theoretic properties of convex-concave two-player zero-sum games are preserved in this generalization.
• Score: 6.129776019898013
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Motivated by Generative Adversarial Networks, we study the computation of Nash equilibrium in concave network zero-sum games (NZSGs), a multiplayer generalization of two-player zero-sum games first proposed with linear payoffs. Extending previous results, we show that various game theoretic properties of convex-concave two-player zero-sum games are preserved in this generalization. We then generalize last iterate convergence results obtained previously in two-player zero-sum games. We analyze convergence rates when players update their strategies using Gradient Ascent, and its variant, Optimistic Gradient Ascent, showing last iterate convergence in three settings -- when the payoffs of players are linear, strongly concave and Lipschitz, and strongly concave and smooth. We provide experimental results that support these theoretical findings.

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