计算正随机博弈与程序静态分析中出现的保序非扩张映射的最小不动点
最优化与控制
2014-02-04 v4
摘要
计算保序映射最小不动点的问题出现在零和正随机博弈的研究中，也出现在通过抽象解释进行的程序静态分析中。在此背景下，折扣率可能为负。我们根据特定半微分的非线性谱半径来刻画不动点的最小性。我们应用这一刻画设计了一种策略迭代算法，该算法适用于有限状态和动作空间的情形。该算法返回一个局部最小不动点，而当折扣率为非负时，该不动点被证明是全局最小的。
引用
@article{arxiv.0806.1160,
title = {Computing the smallest fixed point of order-preserving nonexpansive mappings arising in positive stochastic games and static analysis of programs},
author = {Assalé Adjé and Stéphane Gaubert and Eric Goubault},
journal= {arXiv preprint arXiv:0806.1160},
year = {2014}
}
备注
26 pages, 3 figures. We add new results, improvements and two examples of positive stochastic games. Note that an initial version of the paper has appeared in the proceedings of the Eighteenth International Symposium on Mathematical Theory of Networks and Systems (MTNS2008), Blacksburg, Virginia, July 2008