多臂Bandit过程模型（Multi-armed Bandit Processes,简称为MAB）起源于1950年代，属于动态随机最优化的范畴，是一种特殊类型的动态随机控制模型，用于处理如何最优地进行稀缺资源的分配。从数学上来说，MAB由一组平行的可控随机过程组成，每个随机过程有两个选项：演进和停止，一旦向前演进，该过程的信息会随时更新，同时给出一个报酬流；一旦被停止，则其信息流和报酬都不会发生更新。MAB模型的目标是确定各个随机过程演进和停止的规则（时间分配规则），满足条件：在时间t，各个随机过程进程时间之和不大于总时间t，并且使得期望折扣总报酬达到最大。本项目旨在MAB模型中引入受限策略的概念，以便刻画现实中对策略的技术限制（比如在某个随机过程达到一定的状态时，不允许被停止），相应发展一套受限策略下MAB最优策略的新理论、新方法，并探索其在相关领域比如随机调度领域的应用。

Multi-armed bandit processes (abbreviated as MAB), which are dated back to 1950s, belong to the framework of dynamic stochastic optimizaitons. They are a type of particular dynamic stochastic control models that are concerned with the problems of optimally allocating scareced resources to certain competitive projects. In mathematical language, an MAB constitutes of a set of parallel controllable stochastic processes, each of which has two options: evolution and freezen. Whenever a process evolves, it gives out a flow of rewards. MAB models aim at finding out the rules of evolution and freezen on each controllabel member stochastic processes (time allocation schemes) such that at any calander time t the sum of the time allocated to each projects is not more than t itself, so as to maximize the expected total rewards. The objective of this pproposal is to introduce the concept of restricted policies into the MAB community so as to characterize the restrictions on policies in the real life practice, e.g., freezing is prohibted if the process enters certain particular states, and accordingly develop the optimality theory of MAB under restricted policies, as well as explore the applications of that new theory in related areas including particularly the area of stochastic scheduling.