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arXiv · 2007.05477

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

Amit Kadan·Hu Fu
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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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BibTeXRIS

Amit Kadan, Hu Fu. 2020-07-10. Exponential Convergence of Gradient Methods in Concave Network Zero-sum Games. https://arxiv.org/abs/2007.05477

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