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arXiv 1401.2086cs.GTcs.LGstat.ML
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N人一般和对策中学习Nash均衡的Actor-Critical算法

Actor-Critic Algorithms for Learning Nash Equilibria in N-player General-Sum Games

Astrome Technologies Pvt Ltd(Astrome科技私人有限公司);University of Maryland, College Park(马里兰大学帕克分校);Indian Institute of Science(印度科学学院)

H. L Prasad, L. A. Prashanth, Shalabh Bhatnagar

摘要:

研究了有限折扣一般和随机对策的稳态纳什均衡问题。我们首先将Filar和Vrieze [2004]中的非线性优化问题推广到$N$ -播放器设置,并将此问题分解为更简单的子问题,以确保对于给定的状态和代理没有Bellman错误。然后,我们提供了这些子问题,对应于纳什均衡的基本游戏,并为此目的,我们推导出一组必要和充分的SG-SP(随机游戏子问题)的解点的表征条件。利用这些条件,我们开发了两个演员-评论家算法:OFF-SGSP(基于模型)和ON-SGSP(无模型)。这两种算法都使用一个评论家,估计一个固定的政策和演员,执行下降的政策空间中使用的下降方向,避免局部最小值的价值函数。我们建立,这两种算法收敛,在自我发挥,一定的常微分方程(ODE),其稳定的极限点与固定NE的基本一般和随机游戏的平衡。在一个单一状态的非通用游戏(见Hart和Mas-Colell [2005]),以及在一个合成的两个玩家的游戏设置与$810,000$状态,我们建立了ON-SGSP始终优于NashQ([Hu和Wellman,2003]和FFQ [Littman,2001]算法。

英文摘要:

We consider the problem of finding stationary Nash equilibria (NE) in a finite discounted general-sum stochastic game. We first generalize a non-linear optimization problem from Filar and Vrieze [2004] to a $N$-player setting and break down this problem into simpler sub-problems that ensure there is no Bellman error for a given state and an agent. We then provide a characterization of solution points of these sub-problems that correspond to Nash equilibria of the underlying game and for this purpose, we derive a set of necessary and sufficient SG-SP (Stochastic Game - Sub-Problem) conditions. Using these conditions, we develop two actor-critic algorithms: OFF-SGSP (model-based) and ON-SGSP (model-free). Both algorithms use a critic that estimates the value function for a fixed policy and an actor that performs descent in the policy space using a descent direction that avoids local minima. We establish that both algorithms converge, in self-play, to the equilibria of a certain ordinary differential equation (ODE), whose stable limit points coincide with stationary NE of the underlying general-sum stochastic game. On a single state non-generic game (see Hart and Mas-Colell [2005]) as well as on a synthetic two-player game setup with $810,000$ states, we establish that ON-SGSP consistently outperforms NashQ ([Hu and Wellman, 2003] and FFQ [Littman, 2001] algorithms.

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。

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