Mean-Field Learning：一个调查
Mean-Field Learning: a Survey
摘要：
本文研究了大局中人博弈中平稳均衡的迭代方法。大多数连续动作空间对策的学习算法都局限于严格收缩的最佳对策映射，其中的Banach-Picard迭代以几何收敛速度收敛。当最佳回复图不是收缩时，提出了基于Ishikawa的学习。该算法表现良好的Lipschitz连续和伪压缩映射。然而，收敛速度仍然不能令人满意。提出了几种加速技术。我们解释了如何认知用户可以提高收敛速度的基础上，只有少数测量。该方法在平均场博弈中提供了很好的性能，其中支付函数仅取决于自己的行动和平均场的平均值（一阶矩平均场博弈）。一个学习框架，利用这种游戏的结构，所谓的，平均场学习，提出。所提出的平均场学习框架不仅适用于博弈，而且适用于非凸全局优化问题。然后，我们引入了无反馈的平均场学习，并研究了选美比赛游戏中的均衡收敛，这在金融市场中有着有趣的应用。最后，我们提供了一个完全分布式的平均场学习和它的加速版本，在无线网络中令人满意的解决方案。我们用数值例子说明了收敛速度的提高。
英文摘要：
In this paper we study iterative procedures for stationary equilibria in games with large number of players. Most of learning algorithms for games with continuous action spaces are limited to strict contraction best reply maps in which the Banach-Picard iteration converges with geometrical convergence rate. When the best reply map is not a contraction, Ishikawa-based learning is proposed. The algorithm is shown to behave well for Lipschitz continuous and pseudo-contractive maps. However, the convergence rate is still unsatisfactory. Several acceleration techniques are presented. We explain how cognitive users can improve the convergence rate based only on few number of measurements. The methodology provides nice properties in mean field games where the payoff function depends only on own-action and the mean of the mean-field (first moment mean-field games). A learning framework that exploits the structure of such games, called, mean-field learning, is proposed. The proposed mean-field learning framework is suitable not only for games but also for non-convex global optimization problems. Then, we introduce mean-field learning without feedback and examine the convergence to equilibria in beauty contest games, which have interesting applications in financial markets. Finally, we provide a fully distributed mean-field learning and its speedup versions for satisfactory solution in wireless networks. We illustrate the convergence rate improvement with numerical examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
