论文标题
两人零和游戏的平均场分析
A mean-field analysis of two-player zero-sum games
论文作者
论文摘要
在两人零和连续游戏中找到NASH平衡是机器学习的核心问题，例如用于培训gan和健壮的模型。纯纳什平衡的存在需要强大的条件，而实际上通常不满足。混合的纳什平衡存在于更大的通用性中，可以使用镜下降。然而，这种方法不能扩展到高维度。为了解决这一限制，我们将混合策略作为颗粒的混合物进行参数，其位置和权重更新了梯度下降。我们研究了这种动力学，是与Wasserstein-Fisher-Rao公制的相互作用梯度流相互作用的流量。我们建立了相关的langevin梯度动态的全局收敛到近似平衡。我们证明了将粒子动力学与均值场动力学相关的大量定律。我们的方法确定了高维度的混合平衡，并且对于gan的训练混合物明显有效。
Finding Nash equilibria in two-player zero-sum continuous games is a central problem in machine learning, e.g. for training both GANs and robust models. The existence of pure Nash equilibria requires strong conditions which are not typically met in practice. Mixed Nash equilibria exist in greater generality and may be found using mirror descent. Yet this approach does not scale to high dimensions. To address this limitation, we parametrize mixed strategies as mixtures of particles, whose positions and weights are updated using gradient descent-ascent. We study this dynamics as an interacting gradient flow over measure spaces endowed with the Wasserstein-Fisher-Rao metric. We establish global convergence to an approximate equilibrium for the related Langevin gradient-ascent dynamic. We prove a law of large numbers that relates particle dynamics to mean-field dynamics. Our method identifies mixed equilibria in high dimensions and is demonstrably effective for training mixtures of GANs.
