考虑抽样时间间隔的特殊单臂Bandit报酬过程

应用动态规划向后归纳法和贝叶斯方法,研究了一类特殊单臂Bandit报酬过程的最优决策问题。在这个模型中,未知Bandit过程是抽样时间间隔服从负指数分布,抽样值服从Erlang(2)分布,允许在任意时刻跳转的Bandit报酬过程。讨论了这类Bandit报酬过程Gittins指数的单调性质,并在此基础上将包含这类过程的单臂Bandit报酬过程的最优决策问题简化为一个最优停止问题,构造了计算过程最优停止时间的算法。

Special one-armed Bandit reward process considering random sampling times

The optimal decision problem of a special one-armed Bandit reward process was investigated by using dynamic programming backward induction and the Bayesian approach.This model includes an unknown Bandit reward process with unrestricted switching times,whose random sampling times have a negative exponential distribution and sampling values have an Erlang(2) distribution.The monotonousness of the Gittins index of this Bandit reward process was discussed.Based on the monotonousness,the optimal decision problem of a special one-armed Bandit reward process including this unknown process was simplified to an optimal stopping problem and an algorithm was constructed to compute the optimal stopping times.