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.

中文翻译：

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凹网络零和博弈中梯度方法的指数收敛

受生成对抗网络的启发，我们研究了凹网络零和游戏 (NZSG) 中纳什均衡的计算，NZSG 是首次提出具有线性收益的两人零和游戏的多人泛化。扩展先前的结果，我们表明在这种概括中保留了凸凹两人零和博弈的各种博弈论性质。然后我们概括了先前在两人零和游戏中获得的最后一次迭代收敛结果。我们使用 Gradient Ascent 及其变体 Optimistic Gradient Ascent 分析了玩家更新策略时的收敛率，显示了三种设置中的最后一次迭代收敛——当玩家的收益为线性、强凹和 Lipschitz 以及强凹和平滑时。我们提供支持这些理论发现的实验结果。