二、二、二、一、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、三、三、三、三、三、三、三、三、三、三、三、三、三、三、三、三、三、三、三、三、三、三、三、三、三、三、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、二、后、二、二、二、二、二、二、后、后、后、后、后、更后、更后、更后、更后、一、更 (Second-Order Mirror Descent: Convergence in Games Beyond Averaging and Discounting)

Bolin Gao,Lacra Pavel

from arxiv, 16 pages, 12 figures. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

In this paper, we propose a second-order extension of the continuous-time game-theoretic mirror descent (MD) dynamics, referred to as MD2, which converges to mere (but not necessarily strict) variationally stable states (VSS) without using common auxiliary techniques such as averaging or discounting. We show that MD2 enjoys no-regret as well as exponential rate of convergence towards a strong VSS upon a slight modification. Furthermore, MD2 can be used to derive many novel primal-space dynamics. Lastly, using stochastic approximation techniques, we provide a convergence guarantee of discrete-time MD2 with noisy observations towards interior mere VSS. Selected simulations are provided to illustrate our results.

翻译：在本文中,我们提议将连续时间游戏理论镜像下沉动态(MD2)的第二级扩展,称为MD2,它不使用普通辅助技术(如平均或折扣),而与简单(但不一定严格)的多变稳定状态(VSS)相融合。我们显示,MD2在稍作修改后享有无记录和指数性趋同率,以形成强大的VSS。此外,MD2可以用来产生许多新的原始空间动态。最后,我们采用随机近似技术,提供离散MD2的趋同保证,对内地光是VSS进行噪音观测。我们提供了一些模拟来说明我们的结果。

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