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 provably converges to mere (but not necessarily strict) variationally stable states (VSS) without using common auxiliary techniques such as time-averaging or discounting. We show that MD2 enjoys no-regret as well as an exponential rate of convergence towards strong VSS upon a slight modification. MD2 can also be used to derive many novel continuous-time primal-space dynamics. We then use stochastic approximation techniques to 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)的第二序扩展,称为MD2, 它可以被简单(但不一定严格)稳定变化的状态(VSS)集中起来,而没有使用共同的辅助技术,如时间稳定或贴现等。我们显示MD2享有无回归率,并在稍作修改后获得强大的VSS指数性趋同率。MD2还可以用来获取许多新的连续时间原始空间动态。我们随后使用随机近距离接近技术来提供离散时间MD2的趋同保证,同时对内地光是VSS进行吵闹的观测。我们提供了一些模拟来说明我们的结果。

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